# Mathematical Resources

Please direct suggestions for additional links and reports of broken links to Dr. Chris Hill (chill@sbu.edu).

### St. Bonaventure Resources

**The Mathematics Suite**, which is De La Roche 301, includes resources for job searches, graduate school, summer programs, and the art of problem solving.**The Walter J. O'Brien Mathematics Classroom**, which is De La Roche 106, is equipped with HP Compaq desktop computers featuring Derive, Geometer's Sketchpad, TI-Nspire, TeXstudio, and other mathematics software packages.- Career and Professional Readiness Center
- Friedsam Memorial Library
- MathSciNet (for on-campus users only)
- Computer Science Department
- The Learning Center The Learning Center offers walk-in labs and individual tutoring, all free, for several (mostly 100-level) mathematics courses. The Center is located on the first floor of Plassmann Hall.

### Professional Societies

- Mathematical Association of America (MAA)
- American Mathematical Society (AMS)
- Association for Women in Mathematics (AWM)
- Society for Industrial and Applied Mathematics (SIAM)
- Society for Actuaries (SOA)
- American Statistical Association (ASA)
- National Council of Teachers of Mathematics (NCTM)
- Pi Mu Epsilon (National mathematics honor society)

### Meta-Sites (Compendia of Mathematics-Related Web Sites)

- Math Archives
- Math Forum
- The Mathematical Atlas A collection of short articles designed to provide an introduction to the areas of modern mathematics and pointers to further information.

### Typing Mathematics

- Typing Mathematics: Word, TeX, and PowerPoint This page addresses issues commonly faced by students (particularly St. Bonaventure students) who are writing papers or giving presentations with substantial mathematical content.

### Art and Mathematics

**Architecture**- What Happens When Algorithms Design a Concert Hall? The Stunning Elbphilharmonie. Liz Stinson writes about the design of the new concert hall in Hamburg, Germany for
*Wired*.

- What Happens When Algorithms Design a Concert Hall? The Stunning Elbphilharmonie. Liz Stinson writes about the design of the new concert hall in Hamburg, Germany for
**Crocheting & Knitting**- Woolly Thoughts: In Pursiut of Crafty Mathematics Mathematics through knitting and crochet, by married couple Pat Ashforth and Steve Plummer. Alex Bellos wrote a lovely piece about Ashforth and Plummer's work for
*The Guardian*: Meet the mathekniticians - and their amazing woolly maths creations.

- Woolly Thoughts: In Pursiut of Crafty Mathematics Mathematics through knitting and crochet, by married couple Pat Ashforth and Steve Plummer. Alex Bellos wrote a lovely piece about Ashforth and Plummer's work for
**Multi-media**- Robert Fathauer's art is inspired by mathematics and nature.

**Painting**- Clark Richert turns mathematics and science into art. He has been described as "Colorado’s most important contemporary painter."

**Sculpture**- George Hart is a research professor in the engineering school at Stony Brook University and a freelance mathematical sculptor/designer.
- HYBYCOZO, the Hyperspace Bypass Construction Zone, is a series of large scale polyhedral installations and artworks that investigate geometry through light, shadow, and perception, by Serge Beaulieu and Yelena Filipchuk. The project is inspired by the intersection of math, science, technology, geometry, material, light, and of course, the artists’ favorite book,
*The Hitchhiker’s Guide to the Galaxy*. - Kenneth Snelson pioneered tensegrity, the structural principle of "floating compression." William Grimes discussed Snelson's life and art in an obituary for
*The New York Times*: Kenneth Snelson, Sculptor Who Fused Art, Science and Engineering, Dies at 89.

**Writing**- Why Writers Should Learn Math An article in
*The New Yorker*by Alexander Nazaryan.

- Why Writers Should Learn Math An article in

### Learning and Teaching Mathematics

- Calendar of K-12 Science/Technology/Engineering/Mathematics (STEM) education programs in the Cattaraugus County area.
- National Council of Teachers of Mathematics (NCTM)
*Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States*, by Liping Ma. ISBN-13: 978-0415873840. This outstanding book describes the deep understanding of fundamental mathematics that all elementary teachers need. Ma finds that such profound understanding is more common among Chinese teachers than among U.S. teachers, despite the fact that Chinese teachers receive less formal training than their counterparts in the States. Ma's exceptionally well-written book is highly recommended for any person who teaches or plans to teach K-6 mathematics.- Numberphile This YouTube channel by Brady Haran is filled with accessible, entertaining, and informative videos about numbers.
- 3Blue1Brown This YouTube channel by Grant Sanderson is "some combination of math and entertainment, depending on your disposition. The goal is for explanations to be driven by animations and for difficult problems to be made simple with changes in perspective."
- Success in Mathematics Tips on how to study mathematics, how to approach problem-solving, how to study for and take exams, and when and how to get help.
- Interactive Games & Puzzles Each of these entertaining games and puzzles sharpens problem-solving skills and teaches a bit of mathematics. A Java-enabled browser is required to play along.

### Computing and Graphing

**Computing and graphing resources for Calculus I**- Riemann Sum Calculator Computes Riemann sums and displays the corresponding diagrams.

**Computing and graphing resources for Calculus III**- Isometric (3D) graph paper, courtesy of customgraph.com. Two samples are given below.
- 1&2 per inch isometric 3D light gray & watermark (two-page PDF)
- 2&4 per inch isometric 3D light gray & watermark (two-page PDF)

- 2D Parametric Curve Grapher Graphs parametrically-defined curves in 2d.
- 3D Parametric Curve Grapher (Select "Space curve r(t).") Graphs parametrically-defined curves in 3d. You can rotate the diagram.
- Motion in 3D Graphs a parametrically-defined curve in 3d (or 2d if z is zero), along with velocity and acceleration vectors. You can rotate the diagram.
- 3D Surface Plotter Graphs a single function of two variables. You can rotate or zoom in on the diagram.
- Contour Plotter Plots contour curves for a function of two variables. You can specify the number of contours in the diagram.
- 3D Vector Plotter Plots pairs of vectors in 3d, along with their sum, difference, and cross product. You can rotate or zoom in on the diagram.

- Isometric (3D) graph paper, courtesy of customgraph.com. Two samples are given below.
**Computing resources for statistics**- Correlation and Regression Calculator Computes the correlation coefficient and the regression line and graphs the regression line for a set of data points.

**Free mathematics software packages**(alternatives to excellent but typically expensive programs such as Mathematica, Maple, Matlab, and SPSS)

### Particular Topics

**Culture**- Mathematicians of the African Diaspora A website by Scott W. Williams, professor of mathematics at the University of Buffalo, whose purpose is, in part, to exhibit the inaccuracy of the belief that African Americans cannot succeed in mathematics.

**Geometry**- Platonic Solids in All Dimensions In two dimensions, there are infinitely many regular polygons. In three dimensions, there are just five regular polyhedra, also known as Platonic solids. What happens in four dimensions? Five? Six?
- Scissors Congruence An interactive demonstration of the Wallace–Bolyai–Gerwien Theorem. You draw two simple polygons, and the website shows how they are equidecomposable.
- Wine Bottle Theorem A surprising result about stacking circles, discovered with wine bottles.

**History****Number Theory**- The On-Line Encyclopedia of Integer Sequences
- The Prime Pages Prime number research, records, and resources.
- Pi Day Our Pi Day page includes resources about the amazing number pi and about the day of celebration named for it.
- What's Special About This Number? This site provides one interesting fact for each integer between 0 and 9999.
- What's Special About This Number? Part of the Archimedes Laboratory Project, these pages provide a wealth of interesting facts about many numbers. Caution: Some assertions on these pages are false. (E.g., "The question whether 'zero' is odd or even seems to be totally subjective!" For the record, zero is
*definitely*even, because it's twice an integer.)

**Potpourri****Probability**- Buffon Needle Problem George Reese's discussion of the classic problem in probability, which includes a Java applet for simulating the underlying experiment.

**Projects**- Building a Hexastix A hexastix is a mathematical "sculpture" made from 72 pencils. The pencils are arranged in four interlaced hexagonal rings of 18 pencils. The idea for this amazing project originated with mathematical artist George Hart.
- Building a Tetrablerone A tetrablerone is a mathematical "sculpture" made from 12 Toblerone packages. The unusual shapes of Toblerone packages---long triangular prisms---make them ideal for a very cool (if somewhat expensive) math project. The 12 Toblerones are arranged in four interlaced triangular groups of three.

### Data

- U.S. and World Population Clocks The U.S. Census Bureau provides real-time estimates for the U.S. and world populations. The Census Bureau also provides every U.S. decennial census from the first in 1790 to the most recent.
- How the world went from 170 million people to 7.3 billion, in one map This amazing map animation, created by WorldPopulationHistory.org, shows the growth of humanity over the last 2000 years compressed into three and a half minutes. In the video, the map animation starts at about 1:18 and ends at about 4:48.
- U.S. National Debt Clock This site displays an estimate of the national debt and a wealth of related figures at the second you visit it. The Treasury Department provides daily estimates for the national debt for any business day since 3/31/05 (and monthly or yearly estimates even further back).
- Bank Failures The first graph on this page from the CalculatedRiskBlog displays the number of FDIC-insured bank and thrift failures by year from 1934 to 2017. The economic woes of 2008 and 2009 may lead one to expect that the number of bank failures in these years were the highest since the Great Depression. But as this graph shows, the numbers of bank failures during the S&L crisis of the '80s and '90s were
*much*higher. - United States Presidential Elections Maintained by the Federal Register, this site includes electoral and popular vote tallies for every presidential election, from the first in 1789 to the most recent.
- List of World Records in Athletics This Wikipedia page and its linked pages provide IAAF-sanctioned world records in track and field, road running, and racewalking for men and women.
- Internet Host Count The Internet Systems Consortium provides survey data for the number of Internet hosts from August 1981 through the present year. The number of hosts effectively measures the size of the Internet. Watch the number of hosts grow from 213 in 1981 to over one
*billion*in 2017.

### Data Science

Data Science seeks to draw useful information from large data sets, be they numerical, textual, or visual. It is an amalgam of statistical and machine learning, of data mining and data visualization techniques.

The Harvard Business Review asserts that data scientist will be the sexiest job of the twenty-first century. McKinsey & Company predict a shortage of 175,000 big data professionals by the year 2018.

Applications of data science include...

- helping Netflix, Amazon and Facebook to make the recommendations they do;
- improving the flexibility of the gps system in your auto;
- helping Barack Obama win the presidency;
- providing evidence that Christopher Marlowe coauthored all three “Henry VI” plays;
- refining investment bankers' rates of return in the stock market;
- increasing the survival rates of supremely premature babies.

Curious? Here are a few excellent resources.

- Big Data: A Revolution That Will Transform How We Live, Work, and Think, by Mayer-Schönberger and Cukier.
- Introduction to Data Science, Version 2.0, by Jeffrey Stanton & Robert De Graaf. A free ebook for a free introductory course at Syracuse University.
- Data Smart: Using Data Science to Transform Information into Insight, by John Foreman. Data science in business.
- The Data Journalism Handbook, edited by Jonathan Gray, Liliana Bounegru, and Lucy Chambers. Big Data in Journalism.

### Puzzles and Games

- Mind-Reading Trick This site appears to read your mind... How does it do it? (The trick is based on some elementary number theory.)
- Interactive Games & Puzzles
- MazeWorks.com Java games and puzzles, including the Tower of Hanoi.
- Ed Pegg Jr.'s Math Games A column written for MAA Online (the web site for the Mathematical Association of America). Ed is also the webmaster for MathPuzzle.com.
- MathPuzzle.com An extraordinary collection of mathematical puzzles and links to more mathematical puzzles, maintained by Ed Pegg Jr.
- Ken's Puzzle Links A list of web pages, compiled by Ken Duisenberg, that pose (mostly) mathematical problems for anyone to solve.

### Math in Culture

- Mathematical Quotations
- Mathematical Fiction This well-organized searchable site lists over four hundred works of fiction with mathematical content.
- Mathematics in Movies A collection of movie clips in which mathematics appears.

### Shopping

- MathematiciansPictures.com An online gift shop for people who love math, offering high-quality t-shirts, posters, mugs, greeting cards and more, all with mathematical themes.
- Cafepress.com Math tee-shirts, mugs, and more.
- Zazzle.com Math tee-shirts, mugs, and more.
- World of Escher The definitive source for posters, t-shirts, puzzles, calendars, and other items decorated with the art of M.C. Escher.