Mathematics Research Guide

1. Open Educational Resources (OER)

• OER Commons: A comprehensive digital library of open educational resources, including textbooks and course materials for mathematics.
• OpenStax: Offers free, peer-reviewed textbooks on subjects such as calculus, algebra, and statistics.

2. Online Courses and Lectures

• Coursera: Provides free access to many courses on various math topics from top universities. Auditing courses is often free.
• edX: Similar to Coursera, offering free courses on mathematics from institutions like MIT, Harvard, and others.
• MIT OpenCourseWare: Offers free lecture notes, exams, and videos from MIT's mathematics courses, covering a wide range of topics.
• Khan Academy: Provides a variety of courses on subjects from basic arithmetic to advanced calculus.

3. Textbooks and Reference Materials

• Project Gutenberg: Offers free access to many classic mathematics books and textbooks.
• CK-12 Foundation: Provides free online textbooks and interactive resources on various math topics.

4. Interactive Learning Tools and Videos

• Desmos: A powerful online graphing calculator and interactive math tool.
• GeoGebra: Offers interactive geometry, algebra, statistics, and calculus applications.
• PatrickJMT: A YouTube channel offering video tutorials on a wide range of math topics.
• Numberphile: A YouTube channel with engaging videos about interesting mathematical concepts and problems.

5. Research and Journals

• arXiv: A repository of research papers in mathematics, physics, computer science, and related fields. Many papers are available for free.
• Directory of Open Access Journals (DOAJ): Contains free, full-text, quality-controlled scientific and scholarly journals, including those focused on mathematics.
• Google Scholar: A freely accessible web search engine that indexes scholarly articles across various disciplines, including mathematics.

6. Math Problem Solving and Competitions

• Art of Problem Solving (AoPS): Offers a wealth of resources, including free online books, problem sets, and forums for discussing mathematical problems.
• Project Euler: A collection of challenging mathematical/computer programming problems.

7. Mathematical Software

• SageMath: An open-source mathematics software system that covers many aspects of mathematics, including algebra, calculus, and number theory.
• Wolfram Alpha: An online computational engine that provides answers and explanations to mathematical queries.

8. Professional Organizations and Resources

• American Mathematical Society (AMS): Offers a range of free resources, including articles, research papers, and tools for students and educators.
• Mathematical Association of America (MAA): Provides resources, articles, and problem-solving competitions.

9. Online Math Communities and Forums

• Math Stack Exchange: A question-and-answer site for people studying math at any level.
• Reddit - r/learnmath: A community where users can ask questions and share resources related to learning mathematics.

10. Additional Educational Websites

• Brilliant.org: Offers interactive learning in math and science through problem solving and guided exercises (some content is free).
• Paul’s Online Math Notes: Provides free tutorials and notes on various math subjects, including algebra, calculus, and differential equations.