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donkuri committed Mar 20, 2024
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title: Learn Mathematics
description: A mathematics study plan created to help learn mathematics
description: A mathematics study plan created to help learn mathematics
theme: jekyll-theme-minima
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- [High School Mathematics](#high-school-mathematics)
- [First steps](#first-steps)
- [Calculus](#calculus)
- [Proof Techniques](#proofs)
- [Proof Techniques](#proof-techniques)
- [Set Theory](#set-theory)
- [Mastering the fundamentals](#mastering-the-fundamentals)
- [Building Foundations](#building-foundations)
- [Linear Algebra](#linear-algebra)
- [Real Analysis](#real-analysis)
- [Discrete Mathematics](#discrete-mathematics)
- [Basic Number Theory](#elementary-number-theory)
- [Basic Number Theory](#basic-number-theory)
- [Abstraction and Generalization](#abstraction-and-generalization)
- [Abstract Algebra](#abstract-algebra)
- [General Topology](#general-topology)
- [Vector Analysis](#vector-analysis)
- [Classical Differential Geometry](#classical-differential-geometry)
- [Part II: Electives]
- [Part II: Electives](part-ii-electives)
- [Diving deeper](#diving-deeper)
- [Analysis](#analysis)
- [Fourier Analysis](#fourier-analysis)
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- [Knot Theory](#knot-theory)
- [Homotopy Theory](#homotopy-theory)
- [Differential Geometry](#differential-geometry)
- [Smooth Manifolds](#modern-differential-geometry)
- [Smooth Manifolds](#smooth-manifolds)
- [Riemannian Geometry](#riemannian-geometry)
- [Lie Groups](#lie-groups)
- [Symplectic Geometry](#symplectic-geometry)
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- [Mathematical Logic](#mathematical-logic)
- [Statistics](#statistics)
- [Game Theory](#game-theory)
- [Applications](#applicaitons)
- [Applications](#applications)
- [Physics](#physics)
- [Classical Mechanics](#classical-mechanics)
- [Quantum Mechanics](#quantum-mechanics)
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# Part I: Core Subjects


This part deals with common subjects found in most undergraduate mathematics degree. There isn't really any subject here I would skip, all of them are important in helping you acquire mathematical maturity, as well as a general understanding of the various basic structures in mathematics.

## Discovering the basics


This section is mostly concerned with revisiting things you should have seen in high school, as well as strengthening your mathematical dexterity by introducing proofs into the mix.

### Prerequisites

#### How to Learn

I believe learning how to learn is very important and something that is rarely discussed outright. I suggest following [this course](https://www.coursera.org/learn/learning-how-to-learn?).

#### High school mathematics

### First steps

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