Self-Study Resources for Mathematics
Self-Study Resources for Mathematics
Embarking on a journey to learn mathematics can be both exciting and challenging. This guide provides a curated list of resources to help you get started, even if you only have a high school level of math. These resources include books, YouTube channels, lecture series, and online courses, divided by specific topics.
Table of Contents
- General Mathematics
- Calculus
- Linear Algebra
- Differential Equations
- Probability and Statistics
- Additional Resources
General Mathematics
Books
- “The Art of Problem Solving” by Richard Rusczyk
- A comprehensive series of books that cover a wide range of mathematical topics, perfect for high school students and beyond.
- Amazon Link
- “Precalculus” by Michael Sullivan
- A great book to bridge the gap between high school math and college-level calculus.
- Amazon Link
- “How to Prove It: A Structured Approach” by Daniel J. Velleman
- An excellent introduction to mathematical proofs, providing a clear and structured approach to understanding and constructing proofs.
- Amazon Link
YouTube Channels
- Khan Academy
- Offers a wide range of math tutorials, from basic arithmetic to advanced calculus and beyond.
- PatrickJMT
- Covers a variety of math topics, including calculus, algebra, and statistics.
Calculus
Books
- “Calculus” by James Stewart
- A widely used textbook for learning calculus, suitable for beginners and advanced students alike.
- Amazon Link
YouTube Channels
- Essence of Calculus by 3Blue1Brown
- A visually intuitive series that explains the fundamental concepts of calculus.
- Khan Academy
- Offers comprehensive tutorials on calculus topics.
- Professor Leonard
- Provides detailed lectures on calculus and other math subjects.
Online Courses
- Coursera: Calculus: Single Variable Part 1 - Functions
- An introductory course on single-variable calculus.
- edX: Calculus 1A: Differentiation
- A course that covers the basics of differentiation.
Linear Algebra
Books
- “Linear Algebra Done Right” by Sheldon Axler
- An excellent introduction to linear algebra, focusing on understanding the concepts rather than just computational techniques.
- Amazon Link
YouTube Channels
- 3Blue1Brown: Linear Algebra
- A visually intuitive series that explains the fundamental concepts of linear algebra.
- MIT OpenCourseWare: Linear Algebra
- A complete lecture series on linear algebra by MIT.
Online Courses
- Coursera: Linear Algebra
- A comprehensive course on linear algebra.
- edX: Linear Algebra - Foundations to Frontiers
- A course that covers the foundations of linear algebra.
Differential equations
YouTube Channels
- Differential Equations by 3Blue1Brown
- A visually intuitive series that explains the fundamental concepts of differential equations.
Probability and Statistics
Books
- “Introduction to Probability” by Joseph K. Blitzstein and Jessica Hwang
- A great resource for learning probability, with clear explanations and plenty of examples.
- Amazon Link
YouTube Channels
- StatQuest with Josh Starmer
- Provides clear and engaging explanations of statistics and probability concepts.
- Khan Academy
- Offers tutorials on probability and statistics topics.
Online Courses
- Coursera: Introduction to Probability and Data
- An introductory course on probability and data analysis.
- edX: Introduction to Probability
- A course that covers the basics of probability.
Additional Resources
- Paul’s Online Math Notes
- A comprehensive set of math notes and tutorials covering algebra, calculus, and differential equations.
- Wolfram Alpha
- A powerful computational engine that can help with solving math problems and visualizing concepts.
- Art of Problem Solving
- A community and resource hub for students interested in math competitions and advanced problem-solving.
These resources should provide a solid foundation for anyone interested in learning mathematics, regardless of their current level of expertise. Happy learning!
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