mathematics.md

Mathematics

General Topics

Contents and References

1. 3Blue1Brown: Why Pi: https://www.3blue1brown.com/topics/why-pi
2. 3Blue1Brown Logarithms: https://itempool.com/3b1b/c/6XOc6exC7am and https://itempool.com/3b1b/c/uByeGoOoUqV
3. Princeton's Companion to Mathematics - Some initial topics
4. Concrete Mathematics: Graham, Knuth, and Patashnik.
5. Probability a. https://www.3blue1brown.com/topics/probability

Linear Algebra

Contents and References

1. Linear Algebra by Gilbert Strang: https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/video_galleries/video-lectures/
2. 3Blue1Brown: https://www.3blue1brown.com/topics/linear-algebra
3. No Bullshit Guide to Linear Algebra

Pre-Calculus

Contents and References

• Trignometry and Trignometric Identities
  • 3Blue1Brown Trignometry Fundamentals: https://itempool.com/3b1b/c/XYq2wSLpFf5
  • Plane Trignometry - Loney (very old book).
• Complex Numbers
  • 3Blue1Brown Complex Numbers Fundamentals: https://itempool.com/3b1b/c/osSo1bARsZM
• Euler's Formula: https://itempool.com/3b1b/c/Q9Knk-DJta8
• Geometry of Complex Numbers
  • https://www.3blue1brown.com/topics/geometry

. Linear-Algebra

Calculus

Topics: Limits and Continuity, The Derivative, 6 functions, rules and theorems, The Integration, The fundamental theorem of Calculus, Infinity, Series, Multivariable Calculus, Differential Equations

References:

1. 3Blue1Brown Essence of Calculus: https://www.3blue1brown.com/topics/calculus

2. Gilbert Strang: Highlights of Calculus: https://ocw.mit.edu/courses/res-18-005-highlights-of-calculus-spring-2010/video_galleries/highlights_of_calculus/

3. Gilbert Strang Derivatives: https://ocw.mit.edu/courses/res-18-005-highlights-of-calculus-spring-2010/video_galleries/derivatives/

4. 3Blue1Brown Differential Equations: https://www.3blue1brown.com/topics/differential-equations

5. Multivariable Calculus (Grant Sanderson - 3Blue1Brown): https://www.khanacademy.org/math/multivariable-calculus/thinking-about-multivariable-function#introduction-to-multivariable-calculus

6. Excellent Books:

   a. Calculus Made Easy - Thompson

   b. Calculus by Spivak

   c. Calculus by Gilbert Strang

   d. All the mathematics you missed [But need to know for graduate school] by Thomas Garrity

   e. Elementary Differential Equations and Boundary Value Problems by Boyce et. al.,