# St. Bonaventure University

# Mathematical Resources

Please direct suggestions for additional links and reports of broken links to Dr. Chris Hill.

- St. Bonaventure Resources
- Art
- Blogs, E-zines, & YouTube Channels
- Computing and Graphing
- Culture
- Data
- Data Science
- Geometry
- History
- Meta-Sites (compendia of math-related websites)

## St. Bonaventure Resources

**The Mathematics Suite (De La Roche 301)**contains resources on mathematical careers, graduate school, and problem solving, and houses numerous math texts and journals. The suite is also a comfortable place to study or relax next to the math professors' offices.- Career and Professional Readiness Center
- Friedsam Memorial Library
- MathSciNet (for St. Bonaventure 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.

## Art

**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 Pursuit 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 Pursuit 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**- Mathematical Imagery Mathematicians and artists continue to create strong, stunning works in all media and to explore the visualization of mathematics.
- 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.
- Global Sculpture Park presents "virtual" mathematical sculptures by Anton Bakker. Bakker's art illustrates concepts such as curves, lines, knots, spirals, Möbius strips, and fractals. This website includes an augmented reality (AR) feature: by viewing a sculpture on your smartphone and clicking the “Activate AR” button, your device will put the sculpture within your environment.
- 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

## Blogs, E-zines, & YouTube Channels

- 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."
- AMS Feature Column These essays are designed for those who have already discovered the joys of mathematics as well as for those who are curious about its promise. Each column spotlights math that is useful, fun, inspiring, or startling.
- Math in the Media A survey of math in the news, courtesy of the AMS.
- Mathologer Professor Burkard Polster invites you to "Enter the world of the Mathologer for really accessible explanations of hard and beautiful math(s)."
- Numberphile This YouTube channel by Brady Haran is filled with accessible, entertaining, and informative videos about numbers.
- Quanta Magazine A superb free online magazine dedicated to illuminating math and science research.
- Terence Tao's Math Blog Updates on Tao's research and expository papers, discussion of open problems, and other math-related topics. Tao is one of the world's greatest mathematicians and is exceptionally articulate and generous with his insights.

## Computing and Graphing

**Computing and graphing resources for Calculus I and II**- Direction Field Explorer A great tool for investigating direction fields of first-order differential equations.
- Linear/engineering graph paper, courtesy of customgraph.com. Two samples are given below.
- 5_Per_Inch_Linear_LightGray (two-page PDF)
- 1&5_Per_Inch_Engineering_Gray&LightGray (two-page PDF)

- Riemann Sum Calculator Computes Riemann sums and displays the corresponding diagrams.
- Volumes of solid of revolution by the disk method A Geogebra resource that graphs approximations for solids of revolution using the disk method.

**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)

- CalcPlot3D A great tool for graphing surfaces, contour plots, space curves, vector fields, vectors, and more. Images can be printed or downloaded.
- Desmos 2D Parametric Curve Grapher Graphs parametrically-defined curves in 2d.
- Motion in 3D Graphs a parametrically-defined curve in 3d (or 2d if z is zero), along with velocity and acceleration vectors.
- Academo graphing tools
- 3D Surface Plotter Graphs a single function of two variables.
- Contour Plotter Plots contour curves for a function of two variables.
- 3D Vector Plotter Plots pairs of vectors in 3d, along with their sum, difference, and cross product.

- 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)

## 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.

## 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;
- winning the US 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.

## 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

- Earliest Known Uses of Various Mathematical Symbols
- Earliest Known Uses of Some of the Words of Mathematics
- On This Day This resource, provided by the Mathematical Association of America, presents historical events related to mathematics that occurred on the current day or of any day of the visitor's choosing in the calendar year.

## Meta-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.

## Number Theory

- The On-Line Encyclopedia of Integer Sequences Founded by Neil Sloane, this database is an incredible resource for professional and amateur mathematicians and anyone who enjoys numbers. The site can be searched by leading terms, name, or keyword. Each sequence may be experienced visually (as a graph) or aurally (as music). The database contains over 300,000 entries.
- Numberphile This YouTube channel by Brady Haran is filled with accessible, entertaining, and informative videos about numbers.
- 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? 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.)

## Probability and Statistics

- Buffon Needle Problem George Reese's discussion of the classic problem in probability, which includes a Java applet for simulating the underlying experiment.
- FiveThirtyEight provides data and statistical analyses in politics, economics, and sports. The site was created by Nate Silver, who is the current editor.

## Problem Solving

- Art of Problem Solving Online Problem solving resources for motivated students grades 5–12 and beyond.
- The Tricki A repository of mathematical know-how.

## Professional Societies

- Mathematical Association of America (MAA)
- Seaway Section (the awesome regional section of the MAA to which St. Bonaventure belongs)

- 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)

## 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.
- Card Constructions: Lovely mathematical projects made from playing cards, courtesy of mathematical artist George Hart.
- Two polyhedral constructions. One is a 60-card construction based on the deltoidal hexacontahedron, and the other is a 30-card construction based on the rhombic triacontahedron. These projects are extensions of Hart's "slide-together" geometric paper constructions.
- 12-card Tunnel Cube
- 12-card Star

- Tensegrity structures: polyhedral projects, courtesy of Angela Yu, made of paper straws and rubber bands, based on the principle of tensegrity.

## 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
- 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.

## Shopping

- Cafepress.com Math tee-shirts, mugs, and more.
- Maths Gear Mathematical curiosities, including puzzles, games, and apparel, often relating to math videos by Steve Mould, Matt Parker, and James Grime. Based in the United Kingdom (hence "maths").
- M.C. Escher Collection The definitive source for posters, t-shirts, puzzles, calendars, and other items decorated with the art of M.C. Escher.
- Zazzle.com Math tee-shirts, mugs, and more.

## Teaching

- 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.- 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.

## Typing Mathematics

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

## Visualization

- The Math Images Project is a collection of images in the Swarthmore College website that illustrate and illuminate certain mathematical concepts. Images are accompanied by discussions of the mathematics underlying them.