Mathematics

Overview

Mathematical foundations supporting technical work, intellectual growth, and wisdom accumulation. A 20-course curriculum from college algebra through graduate-level analysis, algebra, topology, and geometry.

Curriculum Roadmap

Tier 1: Undergraduate Foundation

# Course Status Prerequisites Sections

1

College Algebra

Active

—

56

2

Trig & Pre-Calculus

Not Started

College Algebra

35

3

Calculus I (Differential)

Not Started

Trig & Pre-Calculus

40

4

Calculus II (Integral)

Planned

Calculus I

TBD

5

Calculus III (Multivariable)

Planned

Calculus II

TBD

6

Linear Algebra

Planned

College Algebra

TBD

7

Differential Equations

Planned

Calculus II, Linear Algebra

TBD

8

Discrete Mathematics

Planned

College Algebra

TBD

9

Probability & Statistics

Planned

Calculus II

TBD

Tier 2: Upper Undergraduate / Bridge

# Course Status Prerequisites

10

Real Analysis I

Planned

Calculus II, Linear Algebra

11

Abstract Algebra I

Planned

Linear Algebra, Discrete Math

12

Number Theory

Planned

Abstract Algebra I

13

Complex Analysis

Planned

Calculus III, Real Analysis I

14

Topology (Point-Set)

Planned

Real Analysis I

Tier 3: Graduate Core

# Course Status Prerequisites

15

Real Analysis II (Measure Theory)

Planned

Real Analysis I

16

Abstract Algebra II (Galois, Modules)

Planned

Abstract Algebra I

17

Algebraic Topology

Planned

Topology, Abstract Algebra II

18

Differential Geometry

Planned

Calculus III, Linear Algebra, Real Analysis I

19

Partial Differential Equations

Planned

Calculus III, Differential Equations

20

Functional Analysis

Planned

Real Analysis II, Topology

Prerequisite Chain

College Algebra (1)
  ├── Trig & Pre-Calculus (2)
  │     └── Calculus I (3)
  │           ├── Calculus II (4)
  │           │     ├── Calculus III (5)
  │           │     │     ├── Complex Analysis (13)
  │           │     │     ├── Differential Geometry (18)
  │           │     │     └── PDEs (19)
  │           │     ├── Differential Equations (7) ──→ PDEs (19)
  │           │     ├── Probability & Statistics (9)
  │           │     └── Real Analysis I (10)
  │           │           ├── Complex Analysis (13)
  │           │           ├── Topology (14)
  │           │           │     ├── Algebraic Topology (17)
  │           │           │     └── Functional Analysis (20)
  │           │           └── Real Analysis II (15)
  │           │                 └── Functional Analysis (20)
  │           └── Linear Algebra (6)
  │                 ├── Differential Equations (7)
  │                 ├── Abstract Algebra I (11)
  │                 │     ├── Number Theory (12)
  │                 │     └── Abstract Algebra II (16)
  │                 │           └── Algebraic Topology (17)
  │                 ├── Real Analysis I (10)
  │                 └── Differential Geometry (18)
  └── Discrete Mathematics (8)
        └── Abstract Algebra I (11)

Goal Alignment

Primary: Technical Excellence (foundations for cryptography, algorithms, ML)

Secondary:

  • Wisdom Accumulation (mathematical reasoning and proof)

  • Financial Independence (quantitative skills for analysis)

  • Teaching (curriculum for children: K through Calculus)

Applications by Domain

Domain Mathematical Foundation

Cryptography

Number theory, abstract algebra, elliptic curves (finite fields)

Machine Learning

Linear algebra, calculus (gradient descent), probability, functional analysis

Networking

Graph theory, queueing theory (calculus), signal processing (Fourier/trig)

Security

Probability, statistics, entropy (information theory), combinatorics

Systems Engineering

Differential equations, optimization, control theory

Physics

All of it — calculus, linear algebra, PDEs, differential geometry

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