Mathematics is a field of study in which there are always new ideas to explore. Though we understand far more about math than we once did, questions outweigh the answers in many cases. If you're considering a future in mathematics, check out these resources to get an inside peek at the industry.
- National Association of Mathematicians (NAM): This association, founded in 1969, strives to promote scholarship and achievement in mathematics. NAM emphasizes support for minority mathematicians and students. Members have access to a job bank and internship opportunities.
- American Mathematical Society (AMS): This organization promotes public awareness of mathematics research and scholarship, and supports the efforts of math educators. Members may access a job bank or take advantage of networking opportunities at AMS's numerous conferences and meetings.
- Mathematical Association of America (MAA): The MAA strives to promote math education at the undergraduate level. Students and educators are welcomed as members of the MAA, and may enjoy benefits like its job bank, scholarships and professional development events.
- National Council of Teachers of Mathematics (NCTM): This organization is designed to support math educators who teach at all levels through the undergraduate years. Membership includes numerous professional development opportunities, book and media reviews, and admission to the largest mathematics education conference in the U.S.
- Association for Women in Mathematics (AWM): Developed in 1971 to encourage young women to become mathematicians, the AWM promotes equal opportunity in mathematical science. Educators and students at the high school, undergraduate, and graduate-school level are welcome. Members may qualify for scholarships or travel grants, and are able to peruse the online job bank.
- Society for Industrial and Applied Mathematics (SIAM): Applied mathematics is the practical side of math and aims to solve complex problems. SIAM is primarily focused on the development of computational methodologies that are important to mathematics. Members of SIAM may access its digital library or jobs bank, and may attend conferences and professional development workshops.
- Highlights of Calculus: Offered by the Massachusetts Institute of Technology (MIT), this free course is taught by Professor Gilbert Strang. Covered material includes key ideas and their application, derivatives, and differential calculus.
- Modern Algebra: MIT Professor, James McKernan, developed this open course. Facets of algebra that have been applied most practically to today's world are covered. Class material includes ring theory, group theory, and field theory.
- Theory of Numbers: Also offered by MIT, this free online course approaches theory at the undergraduate level. Topics of discussion include continued fractions, irrational numbers, congruences, and quadratic reciprocity.
- Abstract Algebra: As part of Harvard University's Extension Program, Dr. Benedict Gross' lectures on abstract algebra are available for free. Participants study groups, vector spaces, linear algebra, and the theory of fields.
- Introduction to Mathematical Thinking: Stanford University offers this free 10-week course. This class introduces the concept of mathematical thinking in the context of professional problem-solving. The ideal student in this class is a freshman in college; for more advanced students, a condensed 8-week version of the class is available.
- Mathematics and Statistics: Brought to students by Britain's Open University, this class explores the relationship between math and statistical outcomes. Organizing information and applying critical thinking skills to data, class participants learn how to use math to suss out the data.
Open Access Journals
- Proceedings of the AMS, series B: This free journal is a peer-reviewed publication that reports on research activity in both pure and applied mathematics. Published by the AMS, shorter articles appear in the open-source version of this journal, while longer ones appear in the subscriber's version.
- The American Mathematical Monthly: Published by the MAA for its members, this periodical reports on the mathematics profession. Recent topics have included linear algebra, Pascal's Theorem, and the Cuoco Configuration.
- Bulletin of Mathematical Sciences: Content from this peer-reviewed journal is available at no charge. Article topics include classical analysis, number theory, representation theory, and harmonic analysis. The Bulletin publishes annually in three issues.
- Journal of Mathematics: Another peer-reviewed, open-access journal, the Journal covers original research and reviews of current scholarship in mathematics. Recent articles discussed metric divergence measures in credit scoring, convergence theorems, and diffeomorphisms.
- Journal of Mathematics and Statistics: This peer-reviewed journal covers international research in applied mathematics. Recent articles have explored the law of large numbers, solutions for variational inequalities, and the theory of complex probability.
- The College Mathematics Journal: Also published by the MAA, this journal is targeted to educators who specialize in undergraduate mathematics. Articles, problem sets, and media reviews are just a sampling of this journal's content.
- Our Mathematical Universe: My Quest for the Ultimate Nature of Reality: Noted researcher and physics professor, Max Tegmark, offers up his theories on mathematics and the universe. Readers will dip their toes in complementary sciences such as cosmology, quantum physics, and philosophy as Tegmark explains a startling hypothesis.
- Thinking Mathematically, Fifth Edition: Mathematics in the context of real-world applications demonstrates mathematical thinking. Readers are given study tools, problem sets, and practice exams throughout the text.
- Essential Calculus: Early Transcendentals: Author James Stewart breaks down early transcendentals in calculus. Each major concept to be mastered is illustrated through easily understood definitions; thoughtful problem sets help students apply their new knowledge.
- Mathematics for the Non-mathmetician: Designed as a math textbook for liberal arts majors, this book delves into mathematics in the context of history and culture. Writing with sophisticated language and imagery, author Morris Kline illustrates complex mathematics.
- Journey through Genius: The Great Theorems of Mathematics: Mathematics professor, William Dunham, examines renowned mathematical theorems developed throughout the course of time. Historical anecdotes accompany step-by-step proofs of each theorem.
- Naked Statistics: Stripping the Dread from the Data: Author Charles Wheelan takes a humorous look at statistics and mathematics. Raw data and the tools we need to analyze it are explained in plain English, as are the ways to misuse data and improperly interpret it.
- Gödel, Escher, Bach: An Eternal Golden Braid: This Pulitzer Prize winning book has been a bestseller for 20 years. In it, author Douglas Hofstadter delivers mathematical proofs for Godel's Theorem of Incompleteness, Escher's art, and Bach's compositions.
Online Industry Magazines
- Mathematics Magazine: Published by the Mathematics Association of America, this magazine is issued five times per year. A broad range of topics in plain-English language are presented for MAA members' reading pleasure.
- Applied Mathematics and Optimization: This periodical reviews current research in applied mathematics. Recent discussion topics have included Kirchhoff and Euler-Bernoulli equations, linear multivariable regulators, and the limit theorem.
- Analytics Magazine: This bi-monthly publication examines math used in practical application in business. Statistics analysis is used to solve problems in the business sector; therefore, a greater understanding of mathematics will help us analyze the vast amounts of data available to us.
- Plus Magazine: Math is made interesting in this online resource. Using language targeting the casual reader, sophisticated math research and applications are introduced. Podcasts, puzzles, and downloadable books reinforce mathematical concepts, and media reviews may direct you to other sources of information.
- dy/dan: less helpful: is written by mathematics educator and noted speaker, Dan Meyer. Meyer blogs frequently about mathematical concepts and their practical applications.
- Good Math, Bad Math: was created by computer scientist Mark Chu-Carroll. In Good Math segments, he writes enthusiastically about mathematics. In Bad Math segments, he exposes those who use mathematics incorrectly, in order to analyze data or distort the truth.
- AMS Grad Student Blog: Several master's-level student members of the American Mathematical Society blog here on math-related topics. Recent posts have discussed mathematical card games, career advice for a young mathematician, and an industry conference.
- xkcd: This popular webcomic tackles mathematics and science with wit and sarcasm. Site visitors can scroll over each comic and reveal related information, like a citation, definition, or punchline to a joke.
- Tanya Khovanova's Math Blog: A Massachusetts Institute of Technology professor's personal blog, filled with humor and warmth.
- For the Love of Teaching Math: A high school math teacher writes about challenges in the classroom and shares her teaching tips.
Who to Follow on Twitter
- Algebra Fact: algebra, number theory, and miscellaneous math facts are found through this Twitter feed.
- Worldwide Center of Mathematics: strives to make math education accessible and affordable for all students.
- Maths Jam: Mathematics enthusiasts created this space online for other math geeks to meet and mingle. Puzzles, problems, and games are commonly found here.