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Petition to add Courses/texts in Advanced Topics #14

Closed aayushsinha0706 closed 3 years ago

aayushsinha0706 commented 3 years ago

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

  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