- Wolfram Alpha: Ask it just about anything and you'll get an answer. Don't forget to ask some non-math related questions, too.
- SageMath: Open source replacement for Mathematica, Maple, and Matlab. Based on Python. Can be installed on Mac or Linux machines, or run in the cloud on any machine connected to the internet.
- Maxima: Open source computer algebra system that can be installed on any machine.
- Scilab: Open source replacement for Matlab that can be installed on any machine.
- R: Open source software for statistics and graphics.
- LaTeX: Typesetting for math and science. Anyone planning to teach or study math should know \(\LaTeX\) (because \(\frac{x^2}{x+2}\) looks so much better than x^2/(x+2)).

The pages below contain collections of books on most undergraduate math topics:
Books and articles every math student should read:

- Flatland: A Romance of Many Dimensions, by A Square (Edwin A. Abbott)
- Second Revised Edition, 1884
- A short, satirical story about a two dimensional world visited by a three dimensional sphere. Very entertaining, and it may help you to understand the concept of higher dimensions.

- A Mathematician's Apology, by G. H. Hardy
*Cambridge University Press*, 1940- Hardy's justification for devoting his life to mathematics.

- The Unreasonable Effectiveness of Mathematics in the Natural Sciences, by Eugene Wigner
*Communications in Pure and Applied Mathematics*, vol. 13, No. I, February 1960- A brief and interesting essay about the role of mathematics in the natural sciences, particularly physics.

- Harvard Mathematics Review: There's only six issues, but each is filled with articles written by and for undergraduates.
- Rose Hulman Undergraduate Math Journal
- Involve: A math journal that publishes papers with at least one undergraduate author. These may be a little higher level, but a good summary of an article would be a great talk.
- arXiv.org: Open e-print archive with over 100000 articles in physics, 10000 in mathematics, and 1000 in computer science.

The scholarships below are open to current undergraduates (I haven't included any scholarships that are only available to high school students). If you're interested in applying to any program, check the deadlines and requirements on the site - don't depend on what I have here.

- Prospective 7-12 Secondary Teacher Course Work Scholarships, NCTM
- For: Full time college or university sophomores who plan to teach grade 7-12 mathematics.
- Award: Up to $10,000
- Deadline: Early May

- Prospective Middle School Teacher Course Work Scholarships, NCTM
- For: Full time college or university sophomores who plan to teach middle school mathematics.
- Award: Up to $3,000
- Deadline: Early May

- Alice T. Schafer Prize, AWM
- For: Exceptional undergraduate women in mathematics. US citizens only.
- Award: ??
- Deadline: October 1

- SMART Scholarship, DoD
- For: Undergraduates in math (or other STEM field) interested in a career with the Department of Defense after graduation. US citizens only.
- Award: Full scholarship, in exchange for a contract with the DoD
- Deadline: Fall, opens in August

- MSRI-UP Summer Program
- For: Undergraduate students who have completed two years of university-level mathematics courses and would like to conduct research in the mathematical sciences. US Citizens and permanent residents only.
- Award: $3100 stipend, lodging, meals and roundtrip travel to Berkeley, CA
- Deadline: February

- Women in Defense HORIZONS Scholarship
- For: Undergraduate women with junior level status (60+ credits) interested in a career in national security or defense. US citizens only.
- Award: Varies, $500 - $12,000
- Deadline: July

- Liberty Power Bright Horizons Scholarship
- For: Undergraduates in STEM fields with an interest in energy or the environment. US Citizens and permanent residents only.
- Award: $4,000 - $10,000
- Deadline: July

- MAES Scholarship Program for Latinos in Science and Engineering
- For: Undergraduates of Hispanic heritage in STEM fields; open to MAES student members only.
- Award: $1,000 - $4,000
- Deadline: Late September

- Mathematical Association of America (MAA)
- American Mathematical Society (AMS)
- Association for Women in Mathematics (AWM)
- American Statistical Association (ASA)
- National Council of Teachers of Mathematics (NCTM)
- Society of Actuaries
- American Institute of Mathematics (AIM)
- Mathematical Sciences Research Institute (MSRI)
- Society for Industrial and Applied Mathematics (SIAM)
- Math for America

- Stefan Banach (1892 - 1945)

"Mathematics is the most beautiful and most powerful creation of the human spirit." - George Polya (1887 - 1985)

"Mathematics is the cheapest science. Unlike physics or chemistry, it does not require any expensive equipment. All one needs for mathematics is a pencil and paper." - Paul Erdős (1913 - 1996)

"The purpose of life is to prove and conjecture."

"God may not play dice with the universe, but something strange is going on with the prime numbers."

"A mathematician is a device for turning coffee into theorems." - Albert Einstein (1879 - 1955)

"Pure mathematics is, in its way, the poetry of logical ideas."

"Since the mathematicians have invaded the theory of relativity, I do not understand it myself any more." - David Hilbert (1862 - 1943)

"Mathematics is a game played according to certain simple rules with meaningless marks on paper." - Felix Klein (1849 - 1925)

"Everyone knows what a curve is, until he has studied enough mathematics to become confused through the countless number of possible exceptions." - G.H. Hardy (1877 - 1947)

"I am interested in mathematics only as a creative art." - Bertrand Russell (1872 - 1970)

"Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true."

"I like mathematics because it is not human and has nothing particular to do with this planet or with the whole universe - because, like Spinoza'a God, it won't love us in return." - Georg Cantor (1845 - 1918)

"In mathematics, the art of proposing a question must be held of higher value than solving it." - Andre Weil (1906 - 1998)

"God exists since mathematics is consistent, and the Devil exists since we cannot prove it." - Charles Darwin (1809 - 1882)

"Mathematics seems to endow one with something like a new sense."

"A mathematician is a blind man in a dark room looking for a black cat which isn't there."*(There is debate on who actually said this)* - Johann Wolfgang von Goethe (1749 - 1832)

"Mathematicians are like Frenchmen. Whatever you say to them, they translate it into their own language, and forthwith it means something entirely different." - Rene Descartes (1596 - 1650)

"But in my opinion, all things in nature occur mathematically." - Henri Poincare (1854 - 1912)

"Mathematics is the art of giving the same name to different things." - St. Augustine (354 - 430)

"The good Christian should beware of mathematicians and all those who make empty prophecies. The danger already exists that mathematicians have made a covenant with the devil to darken the spirit and confine man in the bonds of Hell." - Marcus du Sautoy (1965 - )

"Mathematics has beauty and romance. It's not a boring place to be, the mathematical world. It's an extraordinary place. It's worth spending time there."

If it's not funny, you just haven't studied enough math ;-)

- Q: What does the 'B.' in Benoît B. Mandelbrot stand for?

A: Benoît B. Mandelbrot - A physicist, a philosopher, and a mathematician are traveling on a train when they cross the border into Scotland. They look out the window and see a single sheep that appears to be black. The philosopher says "Oh, I see the sheep in Scotland are black". The physicist corrects the philosopher's assumption, and explains "All we know is that some sheep in Scotland are black". "No," says the mathematician. "All we know is that there is at least one sheep in Scotland, and that at least one side of that sheep is black."
- A mathematician, unsatisfied with any commercially available options, sets out to design the perfect dining table. First, he designs the best possible table with 1 leg. He then creates the best possible table with \(k+1\) legs, based on the assumption that a perfect table with \(k\) legs exists. Satisfied that the perfect table with \(n\) legs must exist for any \(n\)
- Physics is a game with objectives, but no rules. Mathematics is a game with rules, but no objective.
- Q: Why did the chicken cross the road?

A: The answer is trivial and left to the reader. - A mathematician and a chemist are having dinner in a restaurant when a candle on another table falls over, resulting in a small fire. The chemist runs into the kitchen, grabs a bucket of water, and puts out the fire. A week later, the same mathematician and chemist are enjoying dinner in the same restaurant when yet another candle tips over, causing another small fire. This time, the mathematician runs to the kitchen and grabs a bucket of water, but hands the bucket to the chemist. "What are you doing?" asks the chemist. "I've reduced the problem to one that has been previously solved," answers the mathematician.
- If you must drink, always know your limit and never drink and derive.
- A physicist, a biologist, and a mathematician are enjoying some coffee at a cafe when they notice two people entering a house across the street. A few minutes later, three people leave the house. The physicist remarks that their initial count was incorrect; they must have seen three people enter. The biologist is sure they counted correctly, and explains that they had simply reproduced. The mathematician does not attempt an explanation, but concludes that if one more person enters the house, it will be empty.
- It only takes one person to make a statistically insignificant difference.