Learning Mathematics
1. Pre-Algebra and Arithmetic
- Book: A Course in Arithmetic by Jean-Pierre Serre
- Topics: Basic arithmetic, numbers, integers, prime numbers, simple equations.
2. Algebra
- Book: Algebra: Chapter 0 by Paolo Aluffi
- Topics: Sets, functions, algebraic structures, polynomials, rings, groups, fields.
3. Trigonometry
- Book: Divine Proportions: Rational Trigonometry to Universal Geometry by N.J. Wildberger
- Topics: Trigonometric identities, functions, triangles, unit circle, and geometry.
4. Functions and Analysis
- Book: A Course in Functional Analysis by John B. Conway
- Topics: Limits, continuity, differentiability, functional spaces.
5. Complex Numbers
- Book: Complex Analysis and Algebraic Geometry by Hans Grauert
- Topics: Complex numbers, analytic functions, algebraic structures of complex fields.
6. Geometry
- Book: Elements de Geometrie Algebrique by A. Grothendieck
- Topics: Euclidean and non-Euclidean geometry, algebraic geometry basics.
7. Calculus
- Book: Real and Complex Analysis by Walter Rudin
- Topics: Single-variable and multi-variable calculus, real analysis, integration, differentiation.
8. Set Theory
- Book: Set Theory by Felix Hausdorff
- Topics: Sets, relations, cardinality, ordinals, the axiom of choice, Zermelo-Fraenkel set theory.
9. Advanced Geometry
- Book: Foundations of p-adic Teichmüller Theory by Shinichi Mochizuki
- Topics: Advanced concepts in geometry, p-adic theory.
Applications of Mathematics
10. Physics Applications
- Book: An Introduction to Measure Theory by Terence Tao
- Topics: Measure theory, probability, and its application in physics.
11. Statistics and Probability (Women’s Studies)
- Book: Introduction to Random Signals and Noise by Wim C. van Etten
- Topics: Probability, random processes, signal processing.
12. Algebraic Structures and Number Theory
- Book: A Course in Model Theory by Bruno Poizat
- Topics: Mathematical logic, structures, and formal models.
13. Algebraic Geometry
- Book: Local Fields by Jean-Pierre Serre
- Topics: Number theory, field theory, valuation theory.
14. Advanced Algebra
- Book: Naive Lie Theory by John Stillwell
- Topics: Lie groups, Lie algebras, symmetries in mathematics.
15. Sheaf Theory (Farming)
- Book: Sheaf Theory by Glen E. Bredon
- Topics: Topology, sheaf theory, homological algebra.
16. Computer Science Applications
- Book: An Invitation to C-Algebras* by William Arveson
- Topics: Operator algebras, functional analysis.
17. Spectral Theory (Film Studies)
- Book: Analysis Now by Gert K. Pedersen
- Topics: Spectral theory, functional analysis, operator theory.
18. Category Theory (Psychology of Autism)
- Book: Category Theory by Steve Awodey
- Topics: Abstract algebra, logic, and foundational structures of mathematics.
19. Logic and Set Theory
- Book: Mathematical Logic by W.V. Quine
- Topics: Propositional logic, predicate logic, formal systems.
20. Homology and Topology (Queer Studies, Sexuality, and Feminism)
- Book: Homology by Saunders Mac Lane
- Topics: Topology, homological algebra, and higher-dimensional algebraic structures.
21. Intersection Theory
- Book: Intersection Theory by William Fulton
- Topics: Algebraic geometry, intersection theory, and its applications in mathematics.