Maths

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Algebra (Abstract)

1. Groups

Algebra (Elementary)

1. Functions
   1. Concavity
   2. Exponential Functions
   3. Function Growth Rates
   4. Inverse Functions
2. Inequalities
   1. Chebyshev’s Sum Inequality
   2. Holders Inequality
   3. Jensen’s Inequality
   4. Karamata’s and Muirhead’s Inequalities
   5. Schur’s Inequality
   6. Weighted Power Mean
3. Algebraic Factorisation
4. Polynomials

Algebra (Linear)

1. Change of Basis
2. Determinant
3. Eigen Vectors
4. Linear Transforms
5. Matrices
6. Vectors

Calculus and Real Analysis

1. Continuity
2. Derivatives
3. Differential Equations
   1. Euler’s Method for Approximating Differential Equations
   2. Linear Ordinary Differential Equations
4. Epsilon-Delta Definition of a Limit
5. Intervals
6. Integration
   1. Simpson’s Rule for Approximating Integrals
7. Leibnitz’s Theorem and Nth Derivatives
8. L’Hopitals Rule
9. Series
   1. Series Approximations
10. Volumes of Revolution

Combinatorics and Discrete Maths

1. Combinatorics
2. Graphs
3. Recurrence Relations

Complex Analysis

1. Complex Numbers
2. Complex Plane

Geometry (Euclidean)

1. Conic Sections
2. Euclidean Geometry Basics
3. Polar Coordinates
4. Hyperbolic Trigonometric Functions
5. Trigonometric Functions

Number Theory

1. Arithmetic Functions
2. Bezout’s Identity
3. Divisibility
4. Euclid’s Division Lemma
5. Euler’s Theorem
6. Euler’s Totient Function
7. Fermat’s Little Theorem
8. Floor, Ceiling and Fractional Functions
9. GCD
10. LCM
11. Modular Arithmetic
12. Number Bases
13. Number of Divisors
14. Pell’s Equations
15. Prime Counting Function
16. Sum of Divisors
17. Wilson’s Theorem