**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.