ossu/math

Petition to add Courses/texts in Advanced Topics

aayushsinha0706 opened this issue · 0 comments

aayushsinha0706 commented

Advanced Topics

Mathematical Logic

  1. Logic
    Pre-requisite : Intro to Analysis, Intro To Abstract Algebra (Group Theory)
    I recommend these lectures from UC Berkeley

  2. Set Theory
    Pre-requisite: Intro to Analysis, Intro To Abstract Algebra (Group Theory)
    I recommend these lectures from UC Berkeley

  3. Proofs
    I recommend these lectures

  4. Number Theory
    Pre-requisite : Introduction to Abstract Algebra
    I recommend these lectures from Indian Institute of Technology Bombay

Geometry

  1. Euclidean Geometry
    Pre-requisite: Calculus 1C by MIT
    For Euclidean Geometry I would recommend this Textbook by Anton Petrunin from Pennsylvania State University.

  2. Non-Euclidian Geometry
    Non-Euclidian Geometry can be divided in three parts

  • Projective Geometry
    Recommend Pre-requisite : Linear Algebra
    For Projective Geometry I recommend this textbook and I recommend these lectures as additional supplementary lectures.

  • Hyperbolic Geometry and Elliptic geometry
    Pre-requisite :Linear Algebra and Multivariate Calculus
    I recommend these lectures by UNSW Sydney

  1. Point-Set Topology
    Also Knows as Introductory Topology/General Topology
    Pre-Requisite : Intro to Analysis and Metric Spaces
    Before Point Set Topology I recommend studying Metric Spaces by Oxford Mathematics and then watch these lectures on general topology

Probability and Statistics

  1. Combinatorics
    Pre-requisite: Basic Logic and Set Theory
    I recommend these lectures for Combinatorics

  2. Game Theory
    I recommend this MOOC from Stanford and UBC

Abstract Algebra

  1. Abstract Algebra
    Pre-requisite : Group Theory
    This lecture series was held at liberty University and is in two parts. Abstract Algebra 1 and Abstract Algbera 2

  2. Commutative Algebra
    A petition raised by @Admiraldesvl to add Commutative Algebra into Math Curriculum
    Pre-requisite : Linear Algebra, Abstract Algebra 1 and 2
    I recommend this lecture series and this textbook with it.

  3. Algebraic Geometry
    Pre-requisite : Commutative Algebra
    I recommend this Algebraic Geometry 1 series by Richard E Borcherds from UC Berkeley and also Algebraic Geometry 2

  4. Category Theory
    I will recommend this MOOC by MIT

  5. Topology/Algebraic Topology
    Pre-Requisite : Point-Set Topology/ General Topology
    I recommend this lecture series by Prof NJ Wildberger at UNSW Sydney

Mathematical Analysis

  1. Real Analysis
    Pre-requisite : Introduction to Analysis
    I will recommend the Real Analysis series by IIT Madras Real Analysis Part 1 And Real Analysis part 2

  2. Numerical Analysis
    pre-requisite : Calculus 1C, Linear Algebra, Introduction to Differential Equations and Multivariate Calculus
    Numerical Analysis lecture series by IIT Madras.

  3. Complex Analysis
    Pre-requisite : Real Analysis and Linear Algebra
    I found this lecture by IIT Madras to be good
    An another alternative series can be Complex Analysis Fall 2018

Please add these lectures and texts in math curriculum