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Wireless File Transfer Between Desktop and Mobile
In this thread a few of us were whining about the difficulty of transferring files between a "mobile device" (phone/tablet) and a "real computer," in particular the perceived need to use a USB cable, or sneakernet. I want to briefly describe in this post one way to do it wirelessly that may appeal to Unix users.
First the disclosure that I only very recently began to muck around (somewhat reluctantly) with a mobile device, so maybe this is well known and considered trivial. I also don't know how widely applicable it is. I've tested this only on an Samsung Galaxy Tab4 running Android 4.4.2.
The basic idea is very simple: use FTP over wireless, and there is no need to "root the phone". The desktop computer needs to be running an FTP server. On the Android device, it's possible to set up an "FTP server shortcut," which is basically an item that appears in a file manager's directory listing and represents connecting to an FTP server.
Concerning the FTP server, there are many choices on Unix-like OS's. It could be the base ftpd(8), or from a package like vsftpd or proftpd. It's not too hard to set up a server like this, and if it's configured right files can be moved both to and from it.
On the Android side, the shortcut is added something like this:
Done! You can now move files back and forth over a WiFi connection by Selecting them in the source directory and Moving them to the target, all within My Files. Any type of file can be moved or copied, it doesn't have to be a "picture" or "media file."
The main issue here is perhaps security (isn't it always? ). FTP is not a secure protocol, it's in the clear, so you need to use it in an acceptable environment. The main usage case I have in mind is like this:
{Internet}----[Firewall]==[LAN computers,FTP server]==[AP]....(Android)
Works for me. Comments welcome, including how widely applicable this may be on the mobile side. Discussion of other wireless methods in line with the thread title are also welcome.
Last edited by IdOp; 2nd January 2015 at 12:35 PM. Reason: capitalization, elaborations, correction
I use ES File Explorer, or whatever it's called, and its FTP server. I can give a user name and password, but I don't consider it very secure. For the things I transfer though, I am not overly concerned, and I only use it rarely, turning the FTP server off when done.
There are ssh server and client apps for Android as well--I used one for awhile.
Last edited by scottro; 2nd January 2015 at 03:48 AM.
I use FtpCafe in sftp client mode only. I am very curios to see what you guys have to say about this or any other Android topic as I consider myself totally clueless. My feeling when use Android is that somebody else not me controls hardware, software, and data. This might be an opportunity for NetBSD guys to do something for all of us and port NetBSD on any of Android devices and allow me to remove that Android crap.
My feeling--and I'm not even trying to be funny--is that I'm somewhat embarrassed about it. I feel that I should just have a phone that does nothing but call and possibly text, and held out for years.
The things that I transfer are usually public domain ebooks that I've downloaded, and, at work, on occasion a photo.
My most frequent use of the phone is as an ereader on the train, so even if rooting were 100 percent safe and easy, I probably wouldn't even bother. My aging eyes (and mind?) have too much trouble using it as web browser or ssh client.
I don't think I'm typical though. The vast majority of people I know, including those in my age group, make far more use of their phones as browsers, ssh clients, and so on.
Well I don't own a cellphone, smartphone, ebook, iPad or table like device - and I still fail to see the need or use of any of those things.
But since my daughter has a smartphone I occasionally have to figure these things out (that is after trying to figure out was someone would read a pdf on 3" screen...but...).
I go with allowing ssh access to my machines that way you can use an sFTP client...I'm currently had to deal with wireless laptops but I assume as long as there is an "app" with a sFTP client access it the same thing.
"The basic tool for the manipulation of reality is the manipulation of words. If you can control the meaning of words, you can control the people who must use the words." -Philip K. Dick
Thanks all for the comments, and sorry about the delayed reply, the car wouldn't start this morning and I've been developing plan B ever since.
You could make your own device with a low powered developer board, U.S.B. power supply, and a small TFT screen. But, it would probably cost more and requires some personal ingenuity.
I built a laptop with one, reusing a dead Toughbook (8 hour battery life). I have enough room for a better battery and could see 14 plus hours, but its not that big of a deal to me.
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|Stud Port
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|Short review: Here you have your one stop store for all things tempting and homosexual. There are hundreds of diverse studios and internet-sites represented in this oversized stock of licenced content, and this comes in the form of feed internet sites, DVDs, HD films and galleries. Category lists guarantee you find what you want to see, updates happen every day, there are good quality productions here and easy ways to view it all.

subset: commoncrawl


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A visit to Dr. Wallach's Online Catalog will reveal over 250 individual wellness products. Certainly each has its own application and use and can add to a person's quality of life. However, rather than a scattershot approach, the most efficient, least expensive and logical way to make good use of Dr. Wallach's supplement offerings is to start with the "core" supplements, the three supplements that establish a baseline nutritional foundation of the essential 90. After 90 days of saturating one's system in the essential 90 most people find that they need not pile on with the specialty products. It all depends on the individual, really. If you have neglected your health, over the years, if your diet has been poor, then, perhaps stronger measures will be called for. But see what you get with the essential 90, first, is Dr. Wallach's advice. Keep it simple. Keep it low tech. Keep it safe (the specialty supplements are safe but drugs certainly are not!) and keep it at a relatively low cost.
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Thich Nhat Hanh Practice Group
Mondays, 5:00 – 6:30 pm
facilitated by Vicki Rich, Matthew Regan, and Casey Cassidy
This is a group to start your meditation practice or to enhance your current practice. Like Thich Nhat Hahn's teachings this group will be looking into ways of including Buddhist practice into daily life. We will be sharing our struggles and triumphs with our practice.
This practice session consists of one 25-minute sitting meditation session with a 10 minute walking meditation session. Afterwards, we'll read from one of Thich Nhat Hahn's books. The group will end with dharma sharing/discussion.
All are welcome; no experience necessary.
For more about Thich Nhat Hanh, click here to go to the Plum Village website.
Click here for an audio library of his talks.
If you have questions, please email firstname.lastname@example.com.


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reneJ necesitaba un nuevo diseño de logotipo y lanzó un concurso de diseño en 99designs.
Un ganador ha sido elegido entre 491 diseños de 104 diseñadores freelance.
Young Performance Company is looking for a fresh, simple and unique logo. We are very much open to your creative ideas. We are looking forward to your submits! PLEASE READ ON!
Aspirar Performance Company
Aspirar Performance Company is a young and newly established business. It supports management teams and individual managers to improve their performance - with a pragmatic and simple approach. Aspirar helps clients to be successful and specializes in change management . The company provides performance consulting, performance coaching and interim management to improve performance. (Aspirar = Aspire)
The logo inspires confidence, reliability, professionalism and business success. With Contemporary flair and a corporate and high quality feel. Appeals to both corporate and small businesses, but also to individuals seeking coaching. Will be used on our new website, blog, business card, letterhead and marketing materials.
• 'Aspriar' is the most important part of the brand name and should attract the prominent attention. 'Performance Company' is added to give 'Aspirar' an identification. 'Perfomance Company' should therefore be less prominent than 'Aspirar'. In texts the company will also be referred to as 'Aspirar' (see above).
• The logo can have an icon, but it can also consist of typography only.
• Color scheme: we like logos in orange with grey or black or white.
• BUT: we are very much open to your creative ideas and other color schemes, please surprise us!
• Format: Vector (adobe photoshop or adobe illustrator), JPG and a few more formats; high resolution.
• White backgrounds only.
• No Clipart please.
Descubre cómo funciona un concurso de diseño u obtén más información sobre nuestros servicios de diseño de logo.


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Management Buyout: Management buyout occurs when managers or executives of a company purchase controlling interest in their company from existing shareholders. If management has existing funding sources to pay a premium over the existing fair market value of outstanding shares, the company becomes a private corporation without a majority of shares trading on the market. Motivation for management buyout may include preservation of present management positions, privacy in management operations, or potentially substantial capital gain with future expansion and anticipated profits.
Management Fee: A managment fee is a charge against an investor's assets for the fund manager's services in overseeing the portfolio. The charge is calculated as a fixed percentage of the fund's asset value, usually 1% or less, and terms of the fee should be disclosed in the fund's prospectus.
Mandatory Employee Contribution: While participation in an employee benefit plan is voluntary, some plans, generally some defined benefit plans, require mandatory employee contributions in order to accrue benefits under the plan.
Market Risk: Also called systematic risk, market risk is the portion of a security's risk common to all securities in the same asset class, and it cannot be eliminated through diversification. For example, a market risk associated with investment in stocks is the general tendency of share prices to decrease during an economic downturn.
Market Timing: An investor who practices market timing makes buy-sell decisions by attempting to predict market trends, such as the direction of stock prices, the direction of interest rates, or the condition of the economy. Unlike investors who buy and hold securities with the hope of substantial gains over an extended period of time, market-timing investors actively buy and sell securities, hoping to turn quick profits on short-term price fluctuations.
Maturity: The date of maturity is the date on which a debt becomes due for payment. For example, if a bond has a face value of $1,000 and a 30-year term of maturity, the bondholder should receive $1,000 in 30 years.
Medicaid: Medicaid is a federal program that covers medical expenses for individuals who are financially unable to afford health care.
Medicare: Medicare is a federal program that covers health care for individuals age 65 and over, or individuals with certain disabilities.
Medicare Part D: Medicare Part D is the prescription drug benefit program available to Medicare recipients.
Minimum Participation Requirements: Employer-sponsored retirement plans usually require minimum participation requirements. Generally, a participant must be a full-time employee, 21 years of age, and a one-year tenured employee in order to receive benefits. Employee welfare benefit plans may provide a separate criterion for employee participation.
Monthly Housing Expenses: Monthly housing expenses include the sum of the principal, interest, and taxes a borrower pays towards housing on a monthly basis. This figure is used to determine affordability in relation to total income.
Mortality Table: A mortality table is a statistical table showing the death rate of people at each age, usually expressed as the number of deaths per thousand.
Municipal Bond: This tax-exempt bond may be issued by a state government or agency, or by a town, county, or other political subdivision or district. Interest payments are generally not subject to federal taxes, and they may be exempt from state and local taxes if the bondholder is a resident of the state where the bond was issued.
National Association of Securities Dealers Automated Quotations (NASDAQ): NASDAQ is a computerized system that facilitates trading and provides current price quotes for the most actively traded over-the-counter (OTC) securities.
Net Income: Subtracting total costs, expenses, and taxes from total revenue results in the net income.
Net Worth: The amount of asset value exceeding total liabilities is referred to as net worth.
New York Stock Exchange (NYSE): Also called The Big Board and The Exchange, the NYSE is the oldest and largest stock exchange in the US, listing the country's largest corporations. Memberships are sold to brokers, who buy and sell stocks on the floor of the exchange.
Noncontributory Retirement Plan: A noncontributory retirement plan is a pension plan that is funded only with employer contributions, requiring no employee contributions.
Nonforfeitable: Upon vesting, a benefit of an employee benefit plan becomes nonforfeitable and, thus, payable upon any occurrence listed in the employee contract. Some benefits may be conferred immediately or on a deferred basis.
Nonqualified Plan: A nonqualified plan is a retirement or employee benefit plan that does not meet the requirements of Section 401(a) under the Internal Revenue Code and, therefore, is not eligible for favorable tax treatment.
Notary Public: A notary public is an officer of the public that can authenticate signatories on documents and take depositions or oaths. A state or jurisdiction may authorize an applicant to certify specific documents usually for a term of years. Banks, insurance agencies, legal offices, and government buildings often have persons who are notaries public on staff.
Offering Price: In terms of investing, the offering price is the per-share price at which a stock or mutual fund is offered to the public. Companies going public for the first time will issue shares of stock at an offering price, as will companies who are issuing new shares. The market price, a security's most recent price, may be more or less than the offering price. With no-load funds (mutual funds that do not charge sales commissions, the offering price is the same as the initial market price. With load funds (mutual funds that charge sales commissions), a sales charge is added to the market price to reach the offering price.
Old-Age, Survivors, and Disability Insurance (OASDI): OASDI, also known as Social Security, is a comprehensive federal benefits program that includes retirement benefits, disability income, veteran's pension, public housing, and even the food stamp program. The Social Security tax, which is levied on all self-employed and employed workers, is used to fund the program.
Option: An option gives the buyer the right, but not the obligation, to buy or sell a security at a set price on or before a given date. Investors, not companies, issue options. Investors who purchase "call" options bet the security will be worth more than the price set by the option (the strike price), plus the price they paid for the option itself. Buyers of "put" options bet the security's price will go down below the price set by the option.
Ordinary Income: Income is defined as ordinary if it is derived from normal business activities, such as wages and salary, as distinguished from capital gains earned from the sale of assets.
Over-The-Counter (OTC): A security is considered over-the-counter if it traded in some other context than on a formal exchange, such as the NYSE, TXS, AMEX, etc. Also, OTC refers to a market where transactions are conducted among security dealers over a network of telephone and computer lines, rather than on the floor of an exchange.
Paid-Up Additions: Paid-up additions refer to additional life insurance coverage that is typically purchased with policy dividends. Paid-up additions may have a cash value component in addition to a death benefit.
Par Value: The par value refers to the face value of a stock or bond when issued. The par value may bear little relationship to a security's current market value.
Partnership: A partnership is a contractual association between two or more individuals who share in the management and profitability of a business venture. If the agreement specifically contracts for only an investment obligation, the investor is a limited partner. If responsibilities include management or supervision of operations, the holder of that responsibility is a general partner. Partnerships employ general partners, while limited partners associate through securities transactions.
Past Due: Most lenders allow a specified period after a due date during which payment can be made without penalty. Any amount owed that is not received by the end of this grace period is considered past due. When an account is past due, showing a balance that contains past due funds, the creditor may assess a late fee, or consider the account delinquent and report it to a credit reporting agency.
Patent: A patent is an official license granted by the Patent Office to issue exclusive right to an individual or business, for a specified period of time, for the production or sale of a specific invention, process, or design. The financial value of a patent is the future monetary returns from its economic worth.
Pension: A pension is an employer-provided qualified retirement plan. Examples of pension plans include defined benefit plans, profit sharing plans, bonus plans, employee stock ownership plans (ESOPs), thrift plans, target benefit plans, and money purchase plans.
Permanent Life Insurance: Permanent life insurance is a life insurance policy that does not expire and combines a death benefit with a savings portion. This saving portion can build cash value, which can be borrowed against or withdrawn for cash needs. The two main types of permanent life policies are whole life and universal life.
PITI: PITI refers to the components of a mortgage payment: principal, interest, property taxes, and insurance. Principal is the money used to pay down the balance of the loan, interest is the charge you pay for the opportunity to borrow the money, taxes are the property taxes you pay as a homeowner, and insurance refers to both your property insurance and your private mortgage insurance. Residential mortgage lenders usually require evidence that homeowners have property and casualty insurance if they do not fund the insurance as part of their monthly payment.
Plan Administrator: As designated in the insurance or retirement documents, plan administrators of employee benefit programs maintain government regulations and procedures, and confirm that all participating employees receive annual reports.
Plan Sponsor: A plan sponsor refers to an employer who establishes and perpetuates a qualified employee benefit pension plan. Although ultimately responsible for plan administration, plan sponsors often use outside consultants, corporations, government agencies, or labor organizations to confirm the implementation of Internal Revenue Code regulations and guidelines in plan administration.
Points: In terms of real estate mortgages, points quantify the initial fee charged by the lender, with each point being equal to 1% of the total principal of the loan. For example, on a $100,000 mortgage, four points would cost a borrower $4,000.
Policy: A policy is a legal written document that states the terms of an insurance contract.
Policy Dividend: A policy dividend refers to a refund of part of a life insurance premium that reflects the difference between the premium charged and the insurer's actual cost of providing coverage, if lower than previously anticipated.
Policy Exclusion: A policy exclusion is an item specifically not covered by an insurance policy.
Policy Loan: A policy loan is a loan made by an insurance company, secured by the cash surrender value of a life insurance policy.
Policy Reserves: Policy reserves refer to the funds that a state requires an insurer to hold in order to cover all policy obligations.
Policy Rider: A policy rider is a provision that may be added to an insurance policy, at an additional cost, to increase or limit the benefits the policy otherwise provides.
Policyholder: The policyholder is the person or entity owning an insurance policy. The policyholder is usually the insured but may also be a spouse, business partner, partnership, or corporation.
Portability: Portability refers to the ability of an employee to keep benefits after employment ceases. With a mobile workforce in which employees move from one company to another, portability of employee benefits, especially insurance and retirement plans, is important. Concerns about pre-existing conditions or insurability, as well as vesting schedules of qualified pension plans, are critical factors to an employee who entertains a more lucrative employment opportunity elsewhere.
Portfolio: A portfolio is the combined security holdings of an individual investor or mutual fund. The objective of holding investments in a portfolio is to reduce risk through diversification.
Power of Attorney: This legal document, drafted in accordance with state law, grants a person full or limited powers to perform specified acts or make decisions for another person in the event the grantor is unable to act on his or her own. The power terminates upon the disability of the conveyor, unless it is a "durable" power.
Preferred Stock: Preferred stock is a security representing partial ownership, also called equity, in a corporation. Preferred stock does not confer voting rights, as does common stock, but takes precedence in claims against the company's profits and assets.
Premature or Early Distributions: The Internal Revenue Code (IRC) levies penalties for certain distributions before the age of 59˝ from qualified retirement plans. The IRC, however, provides some specific exceptions that qualify for premature or early distributions without penalty.
Premium: A premium is a periodic payment for an insurance policy.
Premium Loan: A premium loan is a loan made from an insurance policy to cover the premiums.
Prepayment: Prepayment is the ability to repay installment credit before it is due or to pay off a loan before its maturity date. Some loans, particularly mortgages, include prepayment clauses allowing you to repay them in advance of the regular schedule without a penalty.
Prepayment Penalty: On a loan without a prepayment clause, the fee a borrower pays for repaying all or part of the loan before it is due is a prepayment penalty.
Present Value: The present value is the amount a future sum of money is worth today given a specified rate of return. For example, an investment that earns 10% annually and can be redeemed for $1,000 in five years would have a present value of $620. In other words, $620 today will be worth $1,000 in five years at a 10% rate of return.
Price/Earnings Ratio (P/E): Also called the "multiple," the P/E ratio is calculated as a stock's price divided by its earnings per share. This ratio gives investors an idea of how much they are paying for a company's current earnings. For example, a stock selling for $30 a share with earnings per share of $2 has a P/E ratio of 15. In other words, the investor paid $15 for each $1 of earnings. Faster growing, or higher risk, companies generally have higher P/E ratios than slower growing, or less risky, firms.
Primary Beneficiary: The primary beneficiary is the named beneficiary who receives the proceeds of an insurance policy or annuity contract when the insured or annuitant dies.
Prime Rate: The prime rate is a standardized short-term borrowing rate established by the Federal Reserve Board. Most banks use the prime rate and base a loan on the creditworthiness and collateral of bank customers (e.g., prime plus 1% or prime plus 2%).
Principal: The principal can refer to the original amount of money invested in a security, the face value of a bond, or the remaining amount owed on a loan, separate from interest. The term principal can also refer to the owner of a private company or the main party to a financial transaction.
Private Letter Ruling: Upon request, the Internal Revenue Service (IRS) may issue an interpretation of a tax situation in light of a particular individual's circumstances with a private letter ruling judgment. Private letter rulings are nonbinding and not to be seen as a precedent for individuals with seemingly similar circumstances.
Private Mortgage Insurance (PMI): Private mortgage insurance protects the lender in case of default. Lenders typically require borrowers to purchase PMI when the loan-to-value ratio is greater than 80%.
Profit and Loss Statement: Also known as an income statement, the profit and loss statement summarizes the revenues, costs, and expenses incurred during a specific time period. These records show the ability of a company to generate profit by increasing revenue and reducing costs.
Profit-Sharing Plan: A profit-sharing plan is a defined contribution plan in which employers allow employees to share in company profits. The employer's contribution, a percentage of profits generally based on an employee's earnings, may vary from year to year with no minimum required. Funds generally accumulate on a tax-deferred basis until the employee leaves the company or retires. An employee's retirement benefit depends on the amount in his or her account at retirement.
Prohibited Transaction: In terms of Individual Retirement Accounts (IRAs), a prohibited transaction is one forbidden by the Internal Revenue Code. Examples include borrowing against an IRA, using an IRA as collateral, and investing IRA funds in collectibles.
Property: Anything that has a value and is owned is termed property. It may be tangible or intangible (incorporeal), personal or public, or common.
Prospectus: A prospectus is an official document that must be provided (according to Securities and Exchange Commission (SEC) regulations) by the issuer to potential purchasers of a new securities issue. The reports within a prospectus provide information on the financial well being of the issuer and the specifics of the issue itself.
Qualified Plan: A qualified plan is a retirement plan that meets the requirements of Section 401(a) of the Internal Revenue Code, one that is, therefore, eligible for tax-favored treatment.
Quotation: The quotation refers to the highest bid and lowest offer (asked) price currently available for a security. For example, an investor requesting a price on XYZ Company might be quoted "40 to 40˝." This means that the best bid price (the highest price any buyer will pay) is currently $40 a share and the best offer price (the lowest price any seller will accept) is $40.50.
Rate of Return: The rate of return is the gain or loss of an investment over a specified period of time, expressed as a percentage increase over the original investment cost. For stocks, the rate of return is the dividend and capital appreciation. The yield is the rate of return on fixed-income securities. Analysts use the return on equity to compare the rates of return on differing investment vehicles. Accountants use internal rates of return when reviewing investment contracts, budgets, or investment opportunities.
Rated Policy: Also called an "extra risk" policy, a rated policy covers a higher risk for a higher-than-usual premium. For example, an insured person with a dangerous occupation or impaired health condition often has a "rated" policy that costs more to protect the insurer from added risk.
Real Estate Investment Trust (REIT): A REIT is a security that sells like a stock on the major exchanges and invests primarily in real estate through properties and mortgages.
Recapitalization: Recapitalization occurs when a company changes its capital structure by exchanging preferred stock for bonds to reduce taxes or to avoid or emerge from a bankruptcy. Often, new debt (e.g., reorganization bonds) is issued to replace existing debt.
Redemption: Redemption is the repayment of a debt security or preferred stock, either for par value at maturity or for a premium before maturity.
Required Minimum Distribution (RMD): The RMD is the legally required minimum annual amount that must be distributed from a retirement account to an IRA holder or qualified plan participant. RMDs, which are calculated by dividing the year-end account balance by the applicable distribution period or life expectancy, must begin by April 1 of the year following that during which the individual reaches age 70˝.
Revenue: Revenue is the amount of money that a company receives during a given period from the sale of goods and services, before expenses and taxes.
Reverse Mortgage: This type of loan is used to turn home equity into cash. The lender makes regular tax-free payments to the homeowner (borrower), which are usually used to fund retirement needs.
Risk: Risk refers to the quantifiable likelihood of loss or less-than-expected returns. For example, U.S. savings bonds, which are backed by the full faith and credit of the federal government, are considered low risk, where as junk bonds, which are issued by companies with questionable credit, are generally considered high risk. Historic or average returns are often used to measure risk.
Risk Tolerance: Risk tolerance is the measurement of an investor's willingness or ability to handle declines in the value of his or her investment portfolio. For many investors, risk tolerance is an important consideration when developing a diversification strategy for a portfolio.
Rollover: A rollover is a tax-free transfer of funds from one retirement plan to another.
Roth IRA: A Roth IRA is a type of Individual Retirement Account (IRA) in which contributions are nondeductible. Earnings grow tax deferred, and distributions are tax free, provided you have owned the account for five years and are at least age 59˝.
Roth IRA Conversion: This refers to the process of converting an existing IRA into a Roth IRA. Roth conversions have specific income eligibility requirements (through 2009) and income tax consequences.
S Corporation (Subchapter S of the Code): An S corporation is an incorporated business that is a "pass-through" entity for tax purposes.
Salary Reduction Plan: A salary reduction plan is any qualified retirement program in which employees make tax advantaged contributions on a pre-tax basis.
Savings Account: A savings account is an account with a bank or savings and loan company that pays interest on money deposited.
Section 162 (Executive Bonus) Plan: Internal Revenue Code Section 162 provides employers a deduction for trade or business expenses. Through this executive bonus plan, the employee owns a life insurance policy for which the employer pays premiums. Premiums are taxable to the employee.
Secured Card: A secured card is a credit card guaranteed by a deposit in a savings account or certificate of deposit (CD). The credit line usually equals the deposit. If a cardholder defaults on payments, the issuer may apply the deposit toward the balance owed.
Securities and Exchange Commission (SEC): The SEC is the primary federal regulatory agency for the securities industry, whose responsibility is to promote full public disclosure and protect investors against fraudulent and manipulative practices. In addition to regulation and protection, it also monitors corporate takeovers in the US. The SEC is composed of five commissioners appointed by the president and approved by the Senate.
Security Deposit: A security deposit is a type of payment usually required of an individual wishing to secure a personal loan, a rental property, or a later purchase.
Self-Directed IRA (SDA): A self-directed IRA is an individual retirement arrangement that allows a holder a wider choice of investments, including stocks, bonds, mutual funds, and money market funds. SDAs may be opened at institutions with trust powers, state FDIC-insured institutions, federal credit unions, and federally chartered savings banks or savings and loans.
Self-Employment Tax: The self-employment tax is a Social Security tax imposed on self-employed individuals. The self employed need to file a special "Computation of Social Security Self-Employment Tax" (Schedule SE) with their annual Individual Income Tax Return Form 1040.
Seller Financing: Seller financing is a "creative financing" technique in which an owner sells property, usually real estate, directly to a buyer. This technique is often used if the market interest rates are too high for the buyer and the seller does not require principal from the sale. The title or deed transfers only at full payment of the loan, and any foreclosure results in the property reverting to the seller. Seller financing was very popular during the 1980s when real estate values escalated. Buyers used seller financing to arrange "no money down" purchases of real estate.
Settlement Costs: Also called closing costs, these are the expenses involved in transferring real estate to a buyer from a seller. Settlement costs typically include fees or charges for loan origination, discount points, appraisal, property survey, title search, title insurance, deed filing, credit reports, taxes, and legal services. Closing costs do not include points and the cost of private mortgage insurance (PMI).
Share: A share is a certificate representing one unit of ownership in a corporation, mutual fund, or limited partnership.
SIMPLE (Savings Incentive Match Plan for Employees) Plan: A SIMPLE Plan is a retirement plan, which can be set up as a 401(k) or IRA, that allows employee pre-tax contributions and mandatory employer matching contributions. All contributions are immediately vested in a SIMPLE plan.
Simplified Employee Pension Plan (SEP): A SEP is a retirement plan allowing both an employer and an employee to contribute to the employee's Individual Retirement Account (IRA) on a discretionary basis, subject to special rules on eligibility and contributions.
Situs: The term situs refers to the location or position of a property. For intangible property, such as debt, the situs is generally the jurisdiction in which the debt obligation was issued.
Small Business Association (SBA): The SBA is a federal government organization that assists small businesses in providing programs and opportunities to hasten their potential growth and success.
Smart Card: Unlike a debit, charge, or AMT card, the smart card requires a prepayment of a specified amount for the future purchase of goods, services, or admissions. Smart card holders may use the card without debiting a checking account or adding balances to a charge card. Banks, hotels, recreational facilities, and other businesses provide smart card privileges to their customers and guests.
Social Security Tax: Since inception, the Social Security system has been funded by a Social Security Tax, which is paid by both employers and employees. These levies are deposited in trust funds for investment. At various optional retirement ages, employees may qualify for fixed-income payments based on marital status, quarters employed, and wages earned. The self-employed worker has a different contribution schedule, but he or she has equal treatment on all distributions at retirement or disability.
Split-Dollar Life Insurance: A split-dollar life insurance agreement is a contractual arrangement between employer and employee sharing obligations and benefits of a life insurance policy. The shared arrangement may govern the payment of premiums, death proceeds, cash values, dividends, or ownership.
Spousal IRA: A spousal IRA is an individual retirement arrangement for a nonworking spouse funded with contributions from the working spouse. The Internal Revenue Service sets a limit on the combined amount a married couple may contribute to a traditional and spousal IRA.
Standard & Poor's 500 Index (S&P 500): The S&P 500 is an index of 500 of the most widely held common stocks on the New York Stock Exchange (NYSE). It is used as a measure to indicate the overall health of the US stock market.
Stock: A stock is a security representing partial ownership, also called equity, in a corporation. Each stock share represents a proportionate claim against the company's profits and assets. Common stock entitles shareholders to participate in stockholder meetings and to vote for the board of directors. Preferred stock does not confer voting rights, but it takes precedence in claims against profits and assets.
Stock Certificate: This document substantiates the legal ownership of shares of stock in a corporation. Stock certificates are made out to the shareholder or the brokerage firm, and they identify the issuer, the number of shares, the par value, and the stock class. A stock certificate must be endorsed by the shareholder to sell the shares.
Stock Market: The stock market is a general term referring to the organized trading of securities in the various market exchanges and the over the counter (OTC) market.
Stock Purchase Plan: A stock purchase plan is a mechanism for employees to purchase company stock. Increasingly, companies are encouraging employee participation in ownership opportunities. Employees may purchase company stock in Employee Stock Ownership Plans (ESOPs), Dividend Reinvestment Plans (DRIPs), stock options, automatic investment plans, and other creative plans. In theory and practice, employees have the potential of becoming majority stockholders through participation in a stock purchase plan, assuming a viable role in corporate planning.
Stock Split: A stock split is a distribution of additional shares to each stockholder in proportion to the shares the individual already owns. A stock split has no immediate effect on a stockholder's equity. For example, if a stock splits 2-for-1, a shareholder who owns one share with a $100 par value before the split, would own two shares, each with a $50 par value, after the split.
Straight-Term Mortgage: A straight-term mortgage is a mortgage in which the borrowed amount is due at the conclusion of a term, or maturity date.
Survivorship Life Insurance: Also called second-to-die or last-to-die insurance, survivorship life insurance covers the lives of two people and pays benefits when the second person dies. It is often used by couples to fund estate tax liability.
Tangible Asset: A tangible asset refers to anything that has a value and physically exists. Land, machines, equipment, automobiles, and even currencies are examples of tangible assets. On some financial statements, however, a nonmaterial item may often be listed as a tangible asset, such as, a payment to be made on products or goods already delivered.
Tax Credit: A tax credit reduces a taxpayer's taxable amount due dollar-for-dollar. A $1,000 tax credit saves the taxpayer $1,000 in taxes. In many cases, tax credits offer incentive to support social change (e.g., renovation of historical property, jobs for the disadvantaged, research and development, and constructing low-income housing).
Tax Deduction: A tax deduction reduces tax liability by the percentage of the marginal tax bracket for the taxpayer. For example, a $1,000 tax deduction for a taxpayer in the 25% marginal tax bracket saves only $250 in tax (0.25 x $1,000). Allowable deductions include charitable contributions, state and local taxes, and some interest expense.
Tax Lien: A tax lien is a claim against property for unpaid taxes (including city, county, school, estate, income, payroll, property, or sales taxes). A tax lien, which lasts until the claim is satisfied or a statute of limitations takes effect, may make other creditors aware of a delinquent's tax liability.
Tax-Exempt Bond: A tax-exempt bond is a bond issued by a municipal, county, or state government whose interest payments are not subject to tax from federal, state, or local authorities.
Tax-Sheltered Annuity: This type of annuity, often called a TSA, allows employees of government and nonprofit organizations to make pretax contributions to a retirement plan, up to a predefined annual limit.
Taxable Income: Taxable income is a taxpayer's gross income less all allowable adjustments. Incorporated businesses derive net income before taxes after deducting total costs and expenses from gross sales.
Tenants by the Entirety: Spouses commonly use this form of ownership. Each spouse theoretically owns 100% of the property, but complete ownership will pass at the first death to the surviving spouse without tax and probate.
Tenants in Common: Two or more owners having undivided ownership (not necessarily equal) in property are referred to as tenants in common. This form of ownership does not have a "right of survivorship" in the event that one owner dies.
Term Certain: In terms of an annuity contract, the term certain is a payout option that provides income for a specified period of time.
Term Insurance: Term insurance is a type of life insurance that pays benefits only when the insured dies within a specific period. If the insured lives beyond the end of the period, no benefits are payable. Term insurance has no cash value, and premiums traditionally rise with age.
Time Horizon: The time horizon is the projected length of time for which an investor plans to hold investments.
Title: A title is a document that identifies legal ownership of property, and it is used to transfer ownership from a seller to a buyer.
Title Insurance: Title insurance is a form of insurance that protects against loss due to a defect in a real estate title, such as an ownership dispute or a lien against property. A mortgage lender generally stipulates that a borrower must purchase a title insurance policy.
Title Search: A title search is the inspection of city, town, or county records to determine the legal owner of real estate property, as well as any applicable liens, mortgages, or future interests.
Total Disability: For insurance purposes, this classification indicates that a worker cannot complete most job requirements based on a physical or mental disability. In some cases, total disability is immediate subsequent to the loss of sight or limbs. In other situations, an "elimination" period provides a passage of time to confirm the disability status before an individual receives benefits. Private disability plans, employer group disability benefits, and Social Security will provide a percentage replacement of lost income for gainfully employed workers who are experiencing a total disability.
Total Return: Total return is defined as the gross annual yield on an investment, including capital appreciation or distributions, interest, dividends, and personal taxes.
Transaction Fee: A transaction fee is a charge for various credit-related activities, such as receiving a cash advance or using an ATM.
Treasuries: Treasuries are negotiated debt obligations that the United States government regularly offers at public auction through the Federal Reserve Bank. Treasuries have varying maturities and yields. Treasury bills have maturities of less than one year, notes less than ten years, and bonds less than 30 years. Issued treasuries may be purchased in the public marketplace and reflect current yields to maturities.
Treasury Bill: Also called a T-bill, a treasury bill is a negotiable debt obligation, which is issued by the federal government and backed by its full faith and credit, has a maturity of one year or less, and is exempt from state and local taxes. Treasury bills have face values ranging from $10,000 to $1 million, and they sell at a discount based on current interest rates.
Triple Net Lease: A triple net lease is a lease in which the lessee assumes the payments of maintenance and upkeep, taxes, utilities, and insurance. The tenant bears the risks associated with these fluctuating expenses.
Trustee: A trustee is an individual or party responsible for managing a trust on behalf of a beneficiary or beneficiaries. Duties often include holding title to property, distributing assets, and overseeing investments and payments.
Underwriting: Underwriting is the process by which an insurance company determines whether, and on what basis, it can assume the risk of a specific life insurance policy. Also, underwriting is the business of investment bankers, who purchase new issues of securities from a company or government and then resell them to the public.
Unemployment: When a previously employed worker is "laid off" or involuntarily "not in gainful employment," he or she is considered unemployed and possibly eligible for certain state and federal compensation and benefits.
Uniform Gift to Minors Act (UGMA): Also called Uniform Transfer to Minors Act (UTMA) in some states, these laws allow an adult to contribute to a custodial account in a minor's name without having to establish a trust or name a legal guardian.
Uniform Transfer to Minors Act (UTMA): Also called Uniform Gift to Minors Act (UGMA) in some states, these laws allow an adult to contribute to a custodial account in a minor's name without having to establish a trust or name a legal guardian.
Universal Life Insurance: Universal life insurance allows the holder to vary the amount and timing of premiums and to change the death benefit, based on the policyholder's changing needs and circumstances. It is generally considered more flexible than traditional whole life insurance and includes a "cash value" savings feature that may allow certain premium funds the opportunity to earn tax-deferred interest.
Unsecured Debt: This type of debt is not guaranteed by collateral. If the borrower defaults, the issuer has no assets to back up the loan.
Variable Interest Rate: A variable interest rate is one that fluctuates with a measure or an index, such as current money market rates or the lender's cost of funds. Often, variable interest rate loans have a fixed rate for several years and then become variable. The borrower is usually protected from dramatic increases in the loan rate by a "rate cap."
Vesting: Vesting is the process leading to a future event at which time money or property held in trust belongs to a person, though it may not be available for distribution until a future date or occurrence. Vesting usually refers to the scheduled confirmation of ownership rights in qualified employee benefit retirement plans.
Volatility: Volatility refers to the relative rate at which the price of a security moves up and down, found by calculating the annualized standard deviation of daily change in price. The more volatile a security or mutual fund, the more it is subject to rapid and extreme price fluctuations relative to the market.
Voluntary Employee Contribution: An employee may be permitted to make voluntary contributions to a retirement plan, usually unmatched by the employer, in excess of mandatory contributions to his or her plan account. Voluntary employee contributions may be deposited on a pre-tax or post-tax basis that is pre-arranged.
Waiver of Premium: This insurance policy rider allows a policyholder to stop making premium payments if the insured suffers a permanent disability. Generally, there is an additional cost for this rider to become part of a policy.
Whole Life Insurance: Whole life insurance provides coverage for the insured's entire life, provided the policyholder continues to pay the premiums. Premiums generally remain level for the life of the contract. In addition, there is also a cash value component that can be used to help supplement future financial needs.
Withholding: Withholding refers to the process by which an employer deducts a portion of employee wages, usually for income taxes. Employers base the withholding amounts on Form W-4, Employee's Withholding Allowance Certificate, which employees submit when commencing employment. A Treasury account at a bank is the repository for withholding amounts and is a credit toward future tax liability for the calendar year.
Working Capital: During the business life cycle, working capital or money ensures that the business will be able to operate on a daily basis.
Yield: The yield of an investment is its annual gain or loss, generally expressed as a percent. To determine the yield on a bond, divide the amount of interest received from the bond by the amount paid for the bond. For example, suppose an individual paid $5,000 for a bond. At 5% interest, he/she would earn $250 annually in interest income. The yield, $5,000 divided by $250, would be 5%. Similarly, to determine the yield on stocks, divide the dividend received per share by the amount paid per share.
Zero Coupon Bond: A zero coupon bond is a bond that makes no periodic interest payments, but rather sells at a deep discount from its face value. At the maturity date, the investor will receive the face value of the bond, plus the interest that has accrued over a fixed term.
510 Bering Dr. Suite 490 , HOUSTON, TX 77057Phone: 713 877 1717 Fax: 713 877 1719 Email: email@example.comemail@example.com offered through Parkland Securities, LLC.A registered broker/dealer. Member FINRA & SIPC.


text:
DoDo Pets HD by Yijing Niu
by via_web on
December 18, 2012
Filed under App DB, Entertainment, Music, iPad Apps
***Magic Pets have travelled to DoDo Planet,where is summer throughout the year.
Magic Pets are calling you,come to play on the beach with them!
***The game is simple,and you just need to click the pet,if there are more than two
adjacent ones of the same type,they will be eliminated.Finish all the waves of each level,
you will pass.
***Come to try!
Developer Website: http://www.icesources.com


text:
Main navigation | Main content
Allen Goldman
Allen Goldman studies the properties of superconductors and selected magnetic materials in the configuration of thin films.
|a) Flower open magnetization and b vortex closed magnetization cross sections showing the direction of the magnetic moments. b) shows complete magnetic flux closure and explains why the vortex state is nearly invisible to the MFM.
Condensed matter physics, and the closely associated discipline of materials physics, are the largest subfields in physics. Condensed matter research at Minnesota spans a range that includes the strange properties of electricity at nanoscales, to activities that may truly be considered "high science," understanding phenomena such as "superfluids," 3He and 4He.
Condensed matter and materials physics have been the sources of numerous technologies important to daily life. These include compound semiconductor electronics, magnetic and optical storage systems, liquid crystal displays, and semiconductor lasers. Among the many efforts at Minnesota aimed at future technology are the experiments in spintronics, which are attempting to solve problems associated with the coupling of a semiconductor and a ferromagnet. Several of the condensed matter faculty members participate in the Materials Research Science and Engineering Center, a collaborative effort by the University that crosses departmental boundaries.
The condensed matter group at Minnesota investigates a wide range of experimental and theoretical problems in superconductivity and superfluidity, magnetism, mesoscopic physics, liquid crystals, semiconductors, surface physics and complexity.
|Fiona Burnell
|Exotic phases of matter-- phases not described by the conventional Landau classification based on broken symmetries.
|Andrey Chubukov
|Condensed matter theorist working in the area of unconventional behavior or electrons: superconductivity, strongly- correlated electron systems and quantum magnetism
|Paul Crowell
|Spin dynamics and transport in ferromagnets and ferromagnet-semiconductor heterostructures.
|E. Dan Dahlberg
|Rafael Fernandes
|Strongly correlated electron systems. Unconventional superconductivity. Competing phases and emergent order. Disorder effects in quantum phase transitions.
|Eric Ganz
|Calculations of the properties of novel Materials
|Allen Goldman
|Properties of superconductors and selected magnetic materials in the configuration of thin films.
|Martin Greven
|Experimental condensed matter physics. High-temperature superconductivity. Low-dimensional magnetism. Crystal growth of quantum materials. Neutron and X-ray scattering. Charge transport.
|J. Woods Halley
|Condensed matter and chemical physics theory, simulation and experiment with an emphasis on interfaces and models of prebiotic evolution.
|Cheng-Cher Huang
|James Kakalios
|Experimental Condensed Matter: Amorphous Semiconductors, Fluctuation Phenomena in Neurological Systems, Segregation in Granular Media
|Alex Kamenev
|Theoretical condensed matter physics, disordered systems and glasses, field-theoretical treatment of many-body systems, mesoscopic systems, out of equilibrium systems
|Natalia Perkins
|Strongly correlated electron systems. Frustrated magnetism. Orbital physics. Competing phases and emergent order in systems with strong spin-orbit coupling.
|Vlad Pribiag
|My research focuses on quantum electronic transport in low-dimensional materials, and applications to quantum information processing.
|Boris Shklovskii
|Theory of transport and electron-electron correlations in disordered systems, quantum Hall effect, hopping conduction, metal-nonmetal transition and transport in nano-crystal films.
|Oriol T. Valls
|Superconducting and Magnetic Proximity Effects in F/S nanostructures; Exotic forms of superconductivity; Charge and Spin Transport in F/S nanostructures; Superfluid Hydrodynamics; Dynamics of quantum Crystals.
|Jorge Vinals
|Nonlinear dynamics, pattern formation, and chaos in systems driven outside of thermodynamic equilibrium. Topological defect motion in soft matter, including transport.
|Ke Wang
|Novel quantum physics in gate-defined nanostructures on 2D Van der Waals materials
|Michael Zudov
|Quantum transport in two-dimensional systems
|Charles E. Campbell
|The many-body theory and statistical mechanics of quantum spin systems and of strongly correlated quantum fluids.
|Morten Christensen
|Avraham Klein
|Dynamics of strongly correlated systems, classical and quantum hydrodynamics, quantum statistics in disordered systems
|Olesya Koroteeva
|Boyi Yang
|Ionic Liquid Doping of High Tc Cuprates


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- The Garmin is useful, many a time, but in Atlanta (and, in other cities, where I have used it), it has often routed me through some extremely busy, unsafe, streets. I am not sure how Garmin is incorporating feedback from real data (from cyclist who commute, legally (not riding on the sidewalk, against traffic, etc).
- Google Maps is great, but I hate to have to mount my iPhone on the handlebar, for I am not sure I want to buy yet another contraption. I am not wanting to buy a all-weather case for my iPhone and I do not want to expose my iPhone to inclement weather. Another drawback with the iPhone is its pathetic (IMHO) battery life, when using Google Maps or any mapping software. Please note that I do have the biggest and the greatest iPhone, to date; namely, the iPhone 5s.
- Finally, I want simplified directions, when it is not necessary to have the whole shebang. Quite honestly, I seldom look at all the data that my Garmin provides anymore, particularly when I am riding. I want useful info and less noise!
I am pretty psyched about this product. It offers me many of the things I am looking for, in one very innovative, simple to use, yet effective package!
You can read all about this product here.
Below, for my readers convenience, I have provided material from Hammerhead.
Saying more with less
All the information you need in a clear and distilled manner. Hammerhead shows you everything you need to navigate while not distracting you with text, small graphics or the need for headphones. We developed cues and signals; much like those used by race car drivers or fighter pilots. It works well in all light and weather conditions. You can even customize the light array within our app to suit your preferences.
Pull out our app. Discover a great ride based on your preferences: hills, distance, scenery or difficulty. Hammerhead will guide you through the route seamlessly with safe, simple, and intuitive turn-by-turn instructions.
Know an awesome ride? Or the best way to get through a city? Share this knowledge instantly with friends and the community. Our app makes it dead simple to send routes to others. Instead of just talking about it, share that ride that you know so well and get rewarded in the app for your contributions.
Strava, MapMyRide - in real time
We are big fans of Strava, MapMyRide and some of the other biking apps out there. We believe you should experience them in real time. Hammerhead gives you turn-by-turn navigation from the routes and segments that you want to ride from your favorite app.
Compete live
We believe that competing in real time beats waiting to see how you did when you get home. Hammerhead will show you your start, end and goal speed for each moment in a segment, and how far off it you might be. Don't compete blind. Make your efforts count.
Catch friends
Hammerhead guides you to meet up with riding buddies that are out on the roads. Join group rides without having to coordinate meeting times and locations.
Off road
Hammerhead is also at home on the trail. Its internal compass and unique red dot pursuit will guide you through the wilderness. Navigate anywhere from trails to the open desert. All with the same safe and simple turn-by-turn light instructions that you've grown to love on the roads.
Long battery life
Our app is ultra efficient, and your smartphone screen remains off. Your smartphone will run for over 5 hours while working with Hammerhead. As for the device itself,we built in the latest LiPo technology to ensure the Hammerhead will last for over 20 hours before recharging via micro USB.
Highest accuracy location
Because Hammerhead uses your smartphone's GPS system, you get a more accurate GPS reading than you would with most standalone GPS units. Don't stand around waiting to acquire satellites -- go ride. Our app pre-loads route information. Venture into the unknown without needing cell service to navigate.
Bike share
The new bike share systems arising nationwide are awesome. We have designed Hammerhead to be able to snap right onto them and guide you around through the urban maze. Hammerhead will even show you how much time you have left on the bike as well as take you to the nearest available docking station with ease. Make urban bike share a complete solution.
We are close
The Hammerhead is more than a year deep in development and testing. It is a truly unique product - there is simply nothing like it. It solves a really big problem – safer, more efficient bicycle navigation – while being really affordable. We need your support to enable us to scale Hammerhead and get it to you. We have partnered with the best minds in manufacturing and software to get you this revolutionary product for the spring riding season.
Join us
We ask you to do two things:
- Share this page with your friends who bike. They will thank you for putting them at the cutting edge.
- Back it and become one of the first to have social bike navigation.
Together we will unlock the safe, awesome biking routes that are hiding in plain sight.
Thank you!
Piet, Laurence & Raveen
I am looking forward to receiving my Hammerhead device soon and putting it to full use; sharing the data with Hammerhead and helping the bicycling community.
I hope you will share my enthusiasm and back Hammerhead as well.
Peace :)


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Lun Lun the 15-year-old giant Panda who lived in Zoo Atlanta is pregnant with her fourth cub, the zoo announced in a press release.
"We're thrilled about the possibility of a fourth cub for Lun Lun, but we remain cautiously optimistic at this point. Giant panda cubs are extremely fragile, and the chance remains that the fetus does not go to term."
Lun Lun, who was artificially inseminated in March, expects to give birth in 2 or 3 weeks if everything goes well. Her cub would be the first giant panda to ever be born in the United States in 2013.
According to an ultrasound done earlier this week, the fetus is currently 1.08 centimeters long.
Before moving the to Zoo Atlanta, Lun Lun lived in Chengdu and her birth name was Hua Hua. She was was renamed by a Taiwanese rock star, Su Huilun, who "adopted" her at the Chengdu Research Base of Giant Panda Breeding.


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It's been 44 years since "Willy Wonka & the Chocolate Factory" first hit theaters in 1971, and although we as viewers feel lucky to have experienced the film, it's the cast of kids—some of them grandparents now!—from the musical adaptation of Roald Dahl's classic novel who really feel like they've been blessed.
Sitting down with the "Today" show Wednesday, Peter Ostrum (Charlie Buckets), Paris Themmen (Mike Teavee), Julie Dawn Cole (Veruca Salt), Rusty Goffe (an Oompa-Loompa), Denise Nickerson (Violet Beauregarde) and Michael Bollner (Augustus Gloop) couldn't help but gush about being part of the film and how they're all still connected by it.
CLICK: ABC family's 25 days of Christmas movie schedule
U.S. & World
"We think of ourselves as a family, maybe a bit of a dysfunctional family, but a family!" Themmen says with a laugh.
Interestingly enough, most of them (with the exception of Goffe), left the industry after making the film. Ostrum—who is now a veterinarian—says, "Everybody could be so lucky to have an experience like this and then to go in a completely different direction!"
Despite stepping out of the spotlight, they've all remained close because they continue to reunite at different events around the world.
One thing they all remember fondly is working with the great Gene Wilder, who never seemed to grow tired of them. "Five kids clambering all over you, wanting his attention," Cole recalls of filming with him. "There was never any, 'Please don't bother Mr. Wilder.' And we must have been pretty tiresome."
WATCH: Johnny Depp channels Willy Wonka
In general, the all unanimously agree that filming "Willy Wonka" was one of the best times of their lives, and if they could, they'd do it all over again.
"Look I mean, we are the fortunate ones," Nickerson says with a smile. "We're here, and we got to really see it and experience it. And the first thing people do when they find out who we are is they smile."
Cole adds, "We call in the Wonka effect."
Check out more from their interview on the "Today" show.


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text: View bid information detailing the current construction projects for which CDB will be accepting bids in the areas of contractor and architect/engineering services. New project information is posted regularly. Register to electronically receive notifications on bid opening meetings and results as well as contract awards. Although registration is not necessary to view these posting on the website, registration is required to receive email notification as the information becomes available.


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Create an Account - Increase your productivity, customize your experience, and engage in information you care about.
Garland Water Utilities, Garland Power & Light, Environmental Waste Services and Stormwater Management have combined efforts to educate and encourage Garland citizens to conserve water and electricity, recycle responsibly and protect our environment.
Follow us on Twitter @GoGreenGarland.


text:
Indic Studies Foundation
(a California non-Profit Organization)www.indicethos.org
www.vepa.us kaushal's
Srinivasa RamanujanFrontpage Template Resources
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Now a Movie about Srinivasa Ramanujam
The Man who knew Infinity
, so hailed because of his tremendous panache
for working with infinite series
was one of India's greatest mathematical geniuses. He
made substantial contributions to the analytical theory
of numbers and worked on elliptic functions, continued
fractions, and infinite series.
was one of India's greatest mathematical geniuses. He
made substantial contributions to the analytical theory
of numbers and worked on elliptic functions, continued
fractions, and infinite series.
The Institute
of Mathematical Sciences, Madras-600 113.
Srinivasa Ramanujan
(1887-1920) hailed as an all-time great mathematician, like
Euler, Gauss or Jacobi, for his natural genius,
has left behind 4000 original theorems, despite his lack of
formal education and a short life-span. In his formative
years, after having failed in his F.A. (First examination in
Arts) class at College, he ran from pillar to post in search
of a benefactor. It is during this period, 1903-1914, he
kept a record of the final results of his original research
work in the form of entries in two large-sized Note Books.
These were the ones which he showed to Dewan Bahadur
Ramachandra Rao (Collector of Nellore), V. Ramaswamy Iyer
(Founder of Indian Mathematical Society), R. Narayana Iyer
(Treasurer of IMS and Manager, Madras Port Trust), and to
several others to convince them of his abilities as a
Mathematician. The orchestrated efforts of his admirers,
culminated in the encouragement he received from Prof. G.H.
Hardy of Trinity College, Cambridge, whose warm response to
the historic letter of Ramanujan which contained about 100
theorems, resulted in inducing the Madras University, to its
lasting credit, to rise to the occasion thrice - in offering
him the first research scholarship of the University in May
1913 ; then in offering him a scholarship of 250 pounds a
year for five years with 100 pounds for passage by ship and
for initial outfit to go to England in 1914 ; and finally,
by granting Ramanujan 250 pounds a year as an allowance for
5 years commencing from April 1919 soon after his triumphant
return from Cambridge ``with a scientific standing and
reputation such as no Indian has enjoyed before''.
Ramanujan was
awarded in 1916 the B.A. Degree by research of the Cambridge
University. He was elected a Fellow of the Royal Society of
London in Feb. 1918 being a ``Research student in
Mathematics Distinguished as a pure mathematician
particularly for his investigations in elliptic functions
and the theory of numbers'' and he was elected to a Trinity
College Fellowship, in Oct. 1918 (- a prize fellowship worth
250 pounds a year for six years with no duties or condition,
which he was not destined to avail of). The ``Collected
Papers of Ramanujan'' was edited by Profs. G.H.Hardy, P.V.
Seshu Aiyar and B.M. Wilson and first published by Cambridge
University Press in 1927 (later by Chelsea, 1962 ; and by
Narosa, 1987), seven years after his death. His `Lost'
Notebook found in the estate of Prof. G.N. Watson in the
spring of 1976 by Prof. George Andrews of Pennsylvania State
University, and its facsimile edition was brought out by
Narosa Publishing House in 1987, on the occasion of
Ramanujan's birth centenary. His bust was commissioned by
Professors R. Askey, S. Chandrasekhar, G.E. Andrews, Bruce
C. Berndt (`the gang of four'!) and `more than one hundred
mathematicians and scientists who contributed money for the
bust' sculpted by Paul Granlund in 1984 and another was
commissioned for the Ramanujan Institute of the University
of Madras, by Mr. Masilamani in 1994. His original Note
Books have been edited in a series of five volumes by Bruce
C. Berndt (``Ramanujan Note Books'', Springer, Parts I to V,
1985 onwards), who devoted his attention to each and every
one of the three to four thousand theorems. Robert Kanigel
recently wrote a delightfully readable biography entitled :
``The Man who knew Infinity : a life of the Genius
Ramanujan'' (Scribners 1991; Rupa & Co. 1993). Truly, the
life of Ramanujan in the words of C.P. Snow: ``is an
admirable story and one which showers credit on nearly
During his five
year stay in Cambridge, which unfortunately overlapped with
the first World War years, he published 21 papers, five of
which were in collaboration with Prof. G.H. Hardy and these
as well as his earlier publications before he set sail to
England are all contained in the ``Collected Papers of
Srinivasa Ramanujan'', referred earlier. It is important to
note that though Ramanujan took his ``Note Books'' with him
he had no time to delve deep into them. The 600 formulae he
jotted down on loose sheets of paper during the one year he
was in India, after his meritorious stay at Cambridge, are
the contents of the `Lost' Note Book found by Andrews in
1976. He was ailing throughout that one year after his
return from England (March 1919 - April 26, 1920). The last
and only letter he wrote to Hardy, from India, after his
return, in Jan. 1920, four months before his demise,
contained no news about his declining health but only
information about his latest work : ``I discovered very
interesting functions recently which I call `Mock'
theta-functions. Unlike the `False' theta-functions (studied
partially by Prof. Rogers in his interesting paper) they
enter into mathematics as beautifully as ordinary
theta-functions. I am sending you with this letter some
examples ... ''. The following observation of Richard Askey
is noteworthy: ``Try to imagine the quality of Ramanujan's
mind, one which drove him to work unceasingly while deathly
ill, and one great enough to grow deeper while his body
became weaker. I stand in awe of his accomplishments;
understanding is beyond me. We would admire any
mathematician whose life's work was half of what Ramanujan
found in the last year of his life while he was dying''.
As for his place in
the world of Mathematics, we quote Bruce C Berndt: ``Paul Erdos has passed on to us Hardy's personal ratings of
mathematicians. Suppose that we rate mathematicians on the
basis of pure talent on a scale from 0 to 100, Hardy gave
himself a score of 25, Littlewood 30, Hilbert 80 and
Ramanujan 100''. G.H.Hardy, in 1923, edited Chapter XII of
Ramanujan's second Notebook on Hypergeometric series which
contained 47 main theorems, many of them followed by a
number of corollaries and particular cases. This work had
taken him so many weeks that he felt that if he were to edit
the entire Notebooks ``it will take the whole of my
lifetime. I cannot do my own work. This would not be
proper.'' He urged Indian authorities and G.N.Watson and B.M.
Wilson to edit the Notebooks. Watson and Wilson divided the
task of editing the Notebooks - Chapters 2 to 13 were to be
edited by Wilson and Chapters 14 to 21 by Watson.
Unfortunately, the premature death of Wilson, in 1935, at
the age of 38, aborted this effort. In 1957, with monetary
assistance from Sir Dadabai Naoroji Trust, at the instance
of Professors Homi J Bhabha and K. Chandrasekaran, the Tata
institute of Fundamental Research published a facsimile
edition of the Notebooks of Ramanujan in two volumes, with
just an introductory para about them. The formidable task of
truly editing the Notebooks was taken up in right earnest by
Professor Bruce C. Berndt of the University of Illinois, in
May 1977 and his dedicated efforts for nearly two decades
has resulted in the Ramanujan's Notebooks
published by Springer-Verlag in five Parts, the first of
which appeared in 1985. The three original Ramanujan
Notebooks are with the Library of the University of Madras,
some of the correspondence, papers/letters on or about
Ramanujan are with the National Archives at New Delhi and
the Tamil Nadu Archives, and a large number of his letters
and connected papers/correspondence and notes by Hardy,
Watson, Wilson are with the Wren Library of Trinity College,
Cambridge. ``Ramanujan : Letters and Commentary'', by Bruce
C. Berndt and Robert A. Rankin (published jointly by the
American Mathematical Society and London Math. Society,
1995) is a recent publication. The Ramanujan Institute for
Advanced Study in Mathematics of the University of Madras is
situated at a short distance from the famed Marina Beach and
is close to the Administrative Buildings of the University
and its Library. The bust of Ramanujan made by Mr.
Masilamani is housed in the Ramanujan Institute. In 1992,
the Ramanujan Museum was started in the Avvai Kalai Kazhagam
in Royapuram. Mrs. Janakiammal Ramanujan, the widow of
Ramanujan, lived for several decades in Triplicane, close to
the University's Marina Campus and died on April 13, 1994. A
bust of Ramanujan, sculpted by Paul Granlund was presented
to her and it is now with her adopted son Mr. W. Narayanan,
living in Triplicane.
Dictionary of Scientific Biography
Biography in
Encyclopaedia Britannica
G H Hardy,
Ramanujan (Cambridge, 1940).
R A Rankin,
Ramanujan's manuscripts and notebooks, Bull.
London Math. Soc. 14
(1982), 81-97.
R A Rankin,
Ramanujan's manuscripts and notebooks II, Bull.
London Math. Soc. 21
(1989), 351-365.
R Kanigel,
The man who knew infinity : A life of the genius
Ramanujan (New York, 1991).
B Berndt,
Srinivasa Ramanujan, The American Scholar
58 (1989), 234-244.
B Berndt and S
Bhargava, Ramanujan - For lowbrows, Amer. Math.
Monthly 100 (1993),
J M Borwein and
P B Borwein, Ramanujan and pi, Scientific American
258 (2) (1988), 66-73.
S R Ranganathan,
Ramanujan : the man and the mathematician
(London, 1967).
S Ram,
Srinivasa Ramanujan (New Delhi, 1979).
L Debnath,
Srinivasa Ramanujan (1887-1920) : a centennial tribute,
International journal of mathematical education in
science and technology 18
(1987), 821-861.
R A Rankin,
Srinivasa Ramanujan (1887- 1920), International
journal of mathematical education in science and
technology 18 (1987),
861- .
K. Srinivasa
Rao, Srinivasa Ramanujan: a Mathematical Genius
(EastWest Books (Madras) Pvt. Ltd., 1998).
June 1998
Interview with Prof. Bruce
C. Berndt.
The academic lineage of
most eminent scholars can be traced to famous
centres of learning, inspiring teachers or an
intellectual milieu, but Srinivasa Ramanujan,
perhaps the greatest of Indian mathematicians, had
none of these advantages. He had just one year of
education in a small college; he was basically
self-taught. Working in isolation for most of his
short life of 32 years, he had little contact with
other mathematicians.
"Many people falsely
promulgate mystical powers to Ramanujan's
mathematical thinking. It is not true. He has
meticulously recorded every result in his three
notebooks," says Dr. Bruce C. Berndt, Professor of
Mathematics at the University of Illino is, whose 20
years of research on the three notebooks has been
compiled into five volumes.
Between 1903 and 1914,
before Ramanujan went to Cambridge, he compiled
3,542 theorems in the notebooks. Most of the time
Ramanujan provided only the results and not the
proof. Berndt says: "This is perhaps because for him
paper was unaffordable and so he worked on a slate
and recorded the results in his notebooks without
the proofs, and not because he got the results in a
Berndt is the only person
who has proved each of the 3,542 theorems. He is
convinced that nothing "came to" Ramanujan but every
step was thought or worked out and could in all
probability be found in the notebooks. Berndt
recalls Ramanujan's well-known i nteraction with G.H.
Hardy. Visiting Ramanujan in a Cambridge hospital
where he was being treated for tuberculosis, Hardy
said: "I rode here today in a taxicab whose number
was 1729. This is a dull number." Ramanujan replied:
"No, it is a very interestin g number; it is the
smallest number expressible as a sum of two cubes in
two different ways." Berndt believes that this was
no flash of insight, as is commonly thought. He says
that Ramanujan had recorded this result in one of
his notebooks before he cam e to Cambridge. He says
that this instance demonstrated Ramanujan's love for
numbers and their properties.
Although Ramanujan's
mathematics may seem archaic by today's standards,
in many respects he was far ahead of his time. While
the thrust of 20th century mathematics has been on
building general theories, Ramanujan was a master in
finding particular result s which are now recognised
as providing the core for the theories. His results
opened up vistas for further research not only in
mathematics but in other disciplines such as
physics, computer science and statistics.
After Ramanujan's death in
1920, the three notebooks and a sheaf of papers that
he left behind were handed over to the University of
Madras. They were sent to G.N. Watson who, along
with B.M. Wilson, edited sections of the notebooks.
After Watson's death in 1965, the papers, which
contained results compiled by Ramanujan after his
return to India from Cambridge in 1914, were handed
over to Trinity College, Cambridge. In 1976, G. E.
Andrews of Pennsylvania State University
rediscovered the papers at the T rinity College
Library. Since then these papers have been called
Ramanujan's "lost notebook". According to Berndt,
the lost notebook caused as much stir in the
mathematical world as Beethoven's Tenth Symphony did
in the world of Western classical music.
Berndt says that the
"unique circumstances surrounding Ramanujan and his
mathematics" make it very difficult to assess his
greatness among such mathematical giants as Newton,
Gauss, Euler and Reimann. According to Berndt, Hardy
had provided the following assessment of his
contemporary mathematicians on a scale of 0 to 100:
"On the basis of pure talent he gave himself a
rating of 25, his collaborator J. E. Littlewood 30,
German mathematician D. Hilbert 80, and Ramanujan
100." Berndt says that it is not R amanujan's
greatness but only its measure that is in doubt.
Besides the five volumes,
Berndt has written over 100 papers on Ramanujan's
works. He has guided a number of research students
in this area. He now works on Ramanujan's "lost
notebook" and on some other manuscripts and
fragments of notes. Recently in Che nnai to give
lectures on Ramanujan's works at the Indian
Institute of Technology, the Institute of
Mathematical Sciences and the Ramanujan Museum and
Mathematical Centre, Berndt spoke to Asha
Krishnakumar on his work on Ramanujan's notebooks,
the broad areas in mathematics that Ramanujan had
covered, the vistas his work has opened up and the
application of his work in physics, statistics and
Excerpts from the
How did you get
interested in Ramanujan's notebooks?
After my Ph.D. at the
University of Wisconsin, I took my first position at
the University of Glasgow (Scotland) in 1966-67.
Prof. R. A. Rankin was a leader in number theory at
that time. I remember being in Rankin's office in
1967 when he told me about R amanujan's notebooks
for the first time. He said: "I have a copy of the
notebooks published by the Tata Institute of
Fundamental Research, Bombay (Mumbai). Would you be
interested in looking at it?" I said, "No, I am not
interested in it."
I did not think about the
notebooks for some years until early 1974 when I was
on leave at the Institute for Advanced Studies in
Princeton, U.S. In February that year, I was reading
two papers of Emil Grosswald in which he proves some
formulae from Raman ujan's notebooks. I realised I
could prove these formulae as well by using a
theorem I proved two years ago. I did that and then
I was curious to find out whether there were other
formulae in the notebooks that I could prove using
my methods. So, I went to the Princeton University
library and got hold of Ramanujan's notebooks
published by the TIFR. I was thrilled to find out
that I could actually prove some more formulae. But
there were a few thousand others I could not.
I was fascinated with the
notebooks and in the next few years I wrote papers
around the formulae I had proved from the notebooks.
The first was a repository paper on Ramanujan's
theta 2n+1 formula, for which I did a lot of
historical research on other pr oofs of the formula.
This I wrote for a special volume called Srinivasa
Ramanujan's Memorial Volume, published by Jupiter
Press in Madras (Chennai) in 1974. After that,
wherever I went, I was all the time working on, and
proving, the various formulae of Ramanujan's - to be
precise - from Chapter 14 of the second notebook.
Then I wrote a sequel to this.
Let me jump ahead to May
1977, when I decided to try and prove all the
formulae in Chapter 14. I took this on as a
challenge. There were in all 87 results in this
chapter. I worked on this for the next one year. I
took the help of my first Ph.D. student, Ron Evans.
After about a year of
working on this, the famous mathematician George E.
Andrews visited Illinois and told me that he
discovered in the spring of 1976 Ramanujan's "lost
notebook" along with G. N. Watson and B. M. Wilson's
edited volumes on Ramanujan's t hree notebooks and
some of their unpublished notes in the Trinity
College Library. I then got photocopies of
Ramanujan's lost notebook and all the notes of
Watson and Wilson. And so I went to the beginning of
the second notebook.
What does the second
notebook contain?
This is the main notebook
because it is the revised and enlarged version of
the first. I went back to the beginning and went
about working my way through it using Watson and
Wilson's notes when necessary.
How long did you work on
the second notebook?
I really do not know how
many years exactly. But some time in the early 1980s
Walter Kaufmann-Buhler, the mathematics editor of
Springer Verlag in New York, showed interest in
my work and decided to publish it. That had not
occurred to me till the n. I agreed and signed a
contract with Springers.
That was when I started
preparing the results with a view to publishing
them. I finally came out with five volumes; I had
thought it would be three. It also took a much
longer time than I had anticipated.
After I completed 21
chapters of the second notebook, the 100 pages of
unorganised material in the second notebook and the
33 pages in the third had a lot more material. I
also found more material in the first which was not
there in the second. So, I fou nd a lot of new
material. It was 20 years before I eventually
completed all the three notebooks.
Why did you start with
the second notebook and not the first?
I knew that the second was
the revised and enlarged edition of the first. The
first was in a rough form and the second, I was
relatively certain, had most of the things that were
there in the first and a lot more.
What did each notebook
The new results that were
in the second notebook were generally among the
unorganised pages of the first. And the third
notebook was all unorganised. A higher percentage of
the results in the unorganised parts of the second
and the third were new. In oth er words, you got a
higher percentage of new results as you went into
the unorganised material.
What do you mean by new
Results that have not been
got earlier.
What is the percentage
of new results in the notebooks?
Hardy estimated that over
two-thirds of the work Ramanujan did in India was
rediscovered. That is much too high. I found that
well over half is new. It is difficult to say
precisely. I would say that most results were new
because we also have to consider that in the
meantime, from 1920 until I started doing this work,
other people discovered these things. So, I would
say that at least two-thirds of the material was
really new when Ramanujan died.
Ramanujan is popularly
known as a number theorist. Would you give a broad
idea about the results in his notebooks? What areas
of mathematics do they cover?
You are right. To much of
the mathematical world and to the public in general,
Ramanujan is known as a number theorist. Hardy was a
number theorist but he was also into analysis. When
Ramanujan was at Cambridge with Hardy, he was
naturally influenced by him (Hardy). And so most of
the papers he published while he was in England were
in number theory. His real great discoveries are in
partition functions.
Along with Hardy, he found
a new area in mathematics called probabilistic
number theory, which is still expanding. Ramanujan
also wrote sequels in highly composite numbers and
arithmetical functions. There are half a dozen or
more of these papers that ma de Ramanujan very
famous. They are still very important papers in
number theory.
However, the notebooks do
not contain much of number theory. It is, broadly
speaking, in analysis. I will try and break that
down a little bit. I would say that the area in
which Ramanujan spent most of his time, more than
any other, is in elliptic funct ions (theta
functions), which have strong connections with
number theory. In particular, Chapters 16 to 21 of
the second notebook and most of the unorganised
portions of the notebooks are on theta functions.
There is a certain type of theta functions ide ntity
which has applications in other areas of
mathematics, particularly in number theory, called
modular equations. Ramanujan devoted an enormous
amount of effort on refining modular equations.
Ramanujan is also popular
for his approximations to pie. Many of his
approximations came with his work on elliptic
functions. Ramanujan computed what are called class
invariants. Even as he discovered them, they were
computed by a German mathematician, H . Weber, in
the late 19th and early 20th centuries. But
Ramanujan was unaware of this. He computed 116 of
these invariants which are much more complicated.
These have applications not only in approximations
to pie but in many other areas as well.
Have you gone through
every one of the 3,254 entries in the three
notebooks and proved each of them, including in the
unorganised material?
I have gone through every
entry in the notebooks. If a result has already been
proved in the literature, then I just wrote the
entry down and said that proofs can be found in this
literature and so on. But I will also discuss the
relevance in history of the entry.
What are the
applications of Ramanujan's discoveries in areas
such as physics, communications and computer
This is a very difficult
question to answer because of the way mathematics
and science work. Mathematics is discovered and it
is then there for others to use. And you do not
always know who uses it. But I have regular contact
with some physicists who I k now use Ramanujan's
work. They find the results very useful in their own
What are the areas in
physics in which Ramanujan's work is used?
The most famous application
in physics is in the area of statistical mechanics.
Among those who I know have used Ramanujan's
mathematics extensively is W. Backster, the
well-known physicist from Australia. He used the
famous Rogers-Ramanujan identities i n what is
called the hard hexagon model to describe the
molecular structure of a thin film.
Many of Ramanujan's works
are used but his asymptotic formulae have found the
most important application; I first wrote this in
1974 from his notebook.
Then there is a particular
formula of Ramanujan's involving the exponential
function which has been used many times in
statistics and probability. Ramanujan had a number
of conjectures in regard to this formula and one is
still unproven. He made this con jecture in a
problem he submitted to the Indian Mathematical
Society. The asymptotic formula is used, for
instance, in the popular problem: What is the
minimum number of people you can have in a room so
that the probability that two share a common birthd
ay is more than half? I think it is 21, 22 or 23.
Anyway, this problem can be generalised to many
other types of similar problems.
Have you looked at the
lost notebook?
That is what I am working
on now with Andrews. It contains about 630 results.
About 60 per cent of these are of interest to
Andrews. He has proved most of these results. The
other 40 per cent are of great interest to me as
most of them were a continuatio n of what Ramanujan
considered in his other notebooks. So, I began
working on them.
What are your
experiences of working on Ramanujan's notebooks? Do
you think Ramanujan was a freak or a genius or he
had the necessary motivation to write the notebooks?
I think one has to be
really motivated to do the kind of mathematics he
was doing, through either teachers or books. We
understand from Ramanujan's biographers that he was
motivated in particular by two books: S. L. Loney's
Plane Trigonometry and Carr's Synopsis of
Elementary Results in Pure Mathematics (which
was a compilation of 5,000 theorems with a few
proofs) at the age of 12. How much his teachers
motivated him, we really do not know as nothing
about it has been recorded. Reading these book s and
going through the problems must have aroused the
curiosity that he had and inspired him.
He is particularly amazing
because he took off from the little bit he knew and
extended it so much in so many directions, leading
to so many new and beautiful results.
Did you find any results
difficult to decipher in any of Ramanujan's notbooks?
Oh yes. I get stuck all the
time. At times I have no idea where these formulae
are coming from. Earlier, Ron Evans, whom I have
already mentioned as having worked on Chapter 14,
helped me out a number of times. There are times I
would think of a formula over for about six months
or even a year, not getting anywhere. Even now there
are times when we wonder how Ramanujan was ever led
to the formulae. There has to be some chain of
reasoning to lead him to think that there might be a
theorem there. But ofte n this is missing. To begin
with, the formulae look strange but over time we
understand where they fit in and how important they
are than they were previously thought to be.
Did you find any serious
errors in Ramanujan's notebooks?
There are a number of
misprints. I did not count the number of serious
mistakes but it is an extremely small number - maybe
five or ten out of over 3,000 results. Considering
that Ramanujan did not have any rigorous training,
it is really amazing that he made so few mistakes.
Are the methods of
mathematics teaching today motivating enough to
produce geniuses like Ramanujan?
Some like G. E. Andrews
think that much of the reforms have come about
because students do not study as much. This, along
with the advent of computers, has changed things. A
lot of mathematics which can be done by
computations, manipulations and by doing exercises
in high school are now being done using calculators
and computers. And the computer, I do not think,
gives any motivation.
The books on calculus
reform (that is now introduced in the U.S.) include
sections on using a computer. To calculate the limit
of a sequence given by a formula, the book says
press these numbers, x, y and z... Then there
appears a string of numbers that get smaller and
smaller and then you can see that is tends to zero.
But that does not lead to any understanding as to
why they are tending to zero. So, this reasoning,
motivation and understanding of why the sequence
tends to zero is not being taught. I think that is
There seem to be two
schools of thought: one which thinks that the
development of concepts and ideas is important and
the other, like that in India, which thinks that
development of skills is important in teaching
mathematics. Which do you think is m ore important?
I think you cannot have one
without the other. Both must be taught. The tendency
in the U.S. is to move away from skills and rely on
computers. I do not think this is correct because if
you have the skills and understanding, then you can
see if you have made an error in punching in the
computers. Andrews and I have the experience of
students putting down results that are totally
ridiculous because they have not understood what is
going on. They do not even realise that they made
mistakes while punching in the computers. So,
developing skills is absolutely necessary. But on
the other hand if you just go on with the skills and
have no understanding of why you are doing this, you
lose the motivation and it becomes just a mechanical
However, even now there is
a possibility that geniuses like Ramanujan will
emerge. It is important that once you identify such
children, books and material should be found for
them specially. The greatest thing about number
theory in which Ramanujan work ed is that you can
give it to people of all ages to stimulate them.
Number theory has problems that are challenging,
that are not too easy, but yet they are durable and
motivating. A foremost mathematician (Atle Selberg)
and a great physicist (Freeman Dy son) of this
century have said that they were motivated by
Ramanujan's number theory when they were in their
early teens.
It is one of the most romantic
stories in the history of mathematics: in 1913, the English
mathematician G. H. Hardy received a strange letter from an
unknown clerk in Madras, India. The ten-page letter
contained about 120 statements of theorems on infinite
series, improper integrals, continued fractions, and number
theory (Here is a
file with a sample of these results). Every prominent
mathematician gets letters from cranks, and at first glance
Hardy no doubt put this letter in that class. But something
about the formulas made him take a second look, and show it
to his collaborator J. E. Littlewood. After a few hours,
they concluded that the results "must be true because, if
they were not true, no one would have had the imagination to
invent them".
Thus was Srinivasa Ramanujan
(1887-1920) introduced to the mathematical world. Born in
South India, Ramanujan was a promising student, winning
academic prizes in high school. But at age 16 his life took
a decisive turn after he obtained a book titled A
Synopsis of Elementary Results in Pure and Applied
Mathematics. The book was simply a compilation of
thousands of mathematical results, most set down with little
or no indication of proof. It was in no sense a mathematical
classic; rather, it was written as an aid to coaching
English mathematics students facing the notoriously
difficult Tripos examination, which involved a great deal of
wholesale memorization. But in Ramanujan it inspired a burst
of feverish mathematical activity, as he worked through the
book's results and beyond. Unfortunately, his total
immersion in mathematics was disastrous for Ramanujan's
academic career: ignoring all his other subjects, he
repeatedly failed his college exams.
As a college dropout from a poor
family, Ramanujan's position was precarious. He lived off
the charity of friends, filling notebooks with mathematical
discoveries and seeking patrons to support his work. Finally
he met with modest success when the Indian mathematician
Ramachandra Rao provided him with first a modest subsidy,
and later a clerkship at the Madras Port Trust. During this
period Ramanujan had his first paper published, a 17-page
work on Bernoulli numbers that appeared in 1911 in the
Journal of the Indian Mathematical Society. Still no one
was quite sure if Ramanujan was a real genius or a crank.
With the encouragement of friends, he wrote to
mathematicians in Cambridge seeking validation of his work.
Twice he wrote with no response; on the third try, he found
Hardy wrote enthusiastically back
to Ramanujan, and Hardy's stamp of approval improved
Ramanujan's status almost immediately. Ramanujan was named a
research scholar at the University of Madras, receiving
double his clerk's salary and required only to submit
quarterly reports on his work. But Hardy was determined that
Ramanujan be brought to England. Ramanujan's mother resisted
at first--high-caste Indians shunned travel to foreign
lands--but finally gave in, ostensibly after a vision. In
March 1914, Ramanujan boarded a steamer for England.
Ramanujan's arrival at Cambridge
was the beginning of a very successful five-year
collaboration with Hardy. In some ways the two made an odd
pair: Hardy was a great exponent of rigor in analysis, while
Ramanujan's results were (as Hardy put it) "arrived at by a
process of mingled argument, intuition, and induction, of
which he was entirely unable to give any coherent account".
Hardy did his best to fill in the gaps in Ramanujan's
education without discouraging him. He was amazed by
Ramanujan's uncanny formal intuition in manipulating
infinite series, continued fractions, and the like: "I have
never met his equal, and can compare him only with
Euler or
One remarkable result of the
Hardy-Ramanujan collaboration was a formula for the number
p(n) of partitions of a number n. A partition
of a positive integer n is just an expression for
n as a sum of positive integers, regardless of order.
Thus p(4) = 5 because 4 can be written as 1+1+1+1, 1+1+2,
2+2, 1+3, or 4. The problem of finding p(n) was
studied by
Euler, who found a formula for the generating function
of p(n) (that is, for the infinite series whose nth
term is p(n)xn). While this allows
one to calculate p(n) recursively, it doesn't lead to
an explicit formula. Hardy and Ramanujan came up with such a
formula (though they only proved it works asymptotically;
Rademacher proved it gives the exact value of p(n)).
Ramanujan's years in England were
mathematically productive, and he gained the recognition he
hoped for. Cambridge granted him a Bachelor of Science
degree "by research" in 1916, and he was elected a Fellow of
the Royal Society (the first Indian to be so honored) in
1918. But the alien climate and culture took a toll on his
health. Ramanujan had always lived in a tropical climate and
had his mother (later his wife) to cook for him: now he
faced the English winter, and he had to do all his own
cooking to adhere to his caste's strict dietary rules.
Wartime shortages only made things worse. In 1917 he was
hospitalized, his doctors fearing for his life. By late 1918
his health had improved; he returned to India in 1919. But
his health failed again, and he died the next year.
Besides his published work,
Ramanujan left behind several notebooks, which have been the
object of much study. The English mathematician G. N. Watson
wrote a long series of papers about them. More recently the
American mathematician Bruce C. Berndt has written a
multi-volume study of the notebooks. In 1997 The
Ramanujan Journal was launched to publish work "in areas
of mathematics influenced by Ramanujan".
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