Partition Of Mathematics

Undergraduate-Level Mathematics:

1. Calculus and Analysis:

1. Differential Calculus

2. Integral Calculus

3. Multivariable Calculus

4. Sequences and Series

5. Limits and Continuity

2. Linear Algebra:

1. Matrix Operations

2. Vector Spaces

3. Linear Transformations

4. Eigenvalues and Eigenvectors

5. Orthogonality and Inner Product Spaces

3. Discrete Mathematics:

1. Logic and Set Theory

2. Combinatorics

3. Graph Theory

4. Number Theory

5. Discrete Probability

4. Probability and Statistics:

1. Probability Theory

2. Descriptive Statistics

3. Random Variables

4. Statistical Inference

5. Hypothesis Testing

5. Differential Equations:

1. First-Order Differential Equations

2. Second-Order Differential Equations

3. Systems of Differential Equations

4. Laplace Transforms

5. Partial Differential Equations

6. Geometry:

1. Euclidean Geometry

2. Non-Euclidean Geometry

3. Coordinate Geometry

4. Geometric Transformations

5. Conic Sections

7. Algebra:

1. Elementary Algebra

2. Polynomials and Factoring

3. Rational Expressions

4. Exponents and Logarithms

5. Equations and Inequalities

8. Real Analysis:

1. Limits and Continuity

2. Differentiation

3. Riemann Integration

4. Sequences and Series

5. Convergence and Divergence

9. Complex Analysis:

1. Complex Numbers

2. Analytic Functions

3. Contour Integration

4. Residue Theory

5. Conformal Mapping

10. Numerical Methods:

1. Root Finding

2. Interpolation and Approximation

3. Numerical Integration

4. Differential Equations

5. Error Analysis

Graduate-Level Mathematics:

1. Algebra:

1. Group Theory

2. Ring Theory

3. Field Theory

4. Linear Algebraic Groups

5. Homological Algebra

2. Analysis:

1. Real Analysis

2. Complex Analysis

3. Functional Analysis

4. Measure Theory and Integration

5. Harmonic Analysis

3. Geometry and Topology:

1. Differential Geometry

2. Algebraic Topology

3. Differential Topology

4. Riemannian Geometry

5. Topological Manifolds

4. Number Theory:

1. Algebraic Number Theory

2. Analytic Number Theory

3. Diophantine Equations

4. Modular Forms

5. Elliptic Curves

5. Probability and Statistics:

1. Probability Theory

2. Stochastic Processes

3. Statistical Inference

4. Multivariate Analysis

5. Bayesian Statistics

6. Mathematical Logic:

1. Model Theory

2. Set Theory

3. Proof Theory

4. Computability Theory

5. Non-Classical Logics

7. Numerical Analysis:

1. Finite Difference Methods

2. Finite Element Methods

3. Iterative Methods

4. Numerical Linear Algebra

5. Computational Fluid Dynamics

8. Partial Differential Equations (PDEs):

1. Elliptic PDEs

2. Parabolic PDEs

3. Hyperbolic PDEs

4. Nonlinear PDEs

5. Numerical PDEs

9. Algebraic Geometry:

1. Projective Varieties

2. Sheaf Theory

3. Moduli Spaces

4. Intersection Theory

5. Hodge Theory

10. Representation Theory:

1. Lie Algebras

2. Representation of Lie Groups

3. Characters and Representations

4. Quantum Groups – Symmetry in Physics