RFC : Addition of Combinatorial Mathematics

[aayushsinha0706]

Problem: Addition of Prbobaility and Statistics courses in its Advanced Maths

Duration: April 07, 2022.

Background: OSSU promises the equivalent of education an undergraduate education in Mathematics. To evaluate our recommended courses, we use the CUPM 2015 guideline that specifies the number of mathematical areas a student should cover.

We will be referring to Discrete Math and Combinatorics document here.

Two courses that CUPM 2015 recommend to cover combinatorial studies

1. Enumerative Combinatorics
2. Graph Theory

Originally this RFC was meant to propose two courses that were on Coursera but were taken down recently. So I will be referring textbook to cover above material

To cover both these courses a open textbook by Mitchel T. Keller, William T. Trotter is recommended by me

Applied Combinatorics

The book was also used to teach students applied combinatorics to students at Georgia Tech. Few reviews about the textbook can be found here.

Now rest of the courses were inspired by CUPM 2015 Applied Math track and MIT Applied Math Track and are of great quality that cant be ignored

The document can be referred here Applied Mathematics

What CUPM 2015 suggests :

Discrete applied mathematics. This area draws on or includes mathematical programming (in linear, integer, and binary forms), graph and network theory, scheduling, error correction systems, data compression systems, etc. Because discrete applied mathematics has emerged relatively recently, courses related to that field may have a greater variety of titles than we find in classical applied mathematics. These include Cryptography, Operations Research (which may also includes tools from continuous mathematics), Discrete Optimization, Linear Programming, Network Science, Graph Theory, Combinatorics, Game Theory, Social Choice, etc.

MIT offeres following in their applied math curriculum as electives

1. Algebraic Combinatorics
2. Analysis of Algorithms
3. Analytic Combinatorics
4. Combinatorial Optimization

ALGEBRAIC COMBINATORICS

This course is offered by premier institutes of India i.e, Institute of Mathematical Sciences with Indian Institute of Technology Madras. The course is short and is of 7 weeks meant to prepare students for post-grad school and is more math-oriented course rather than applied math course.

Algebraic Combinatorics

ANALYSIS OF ALGORITHMS AND ANALYTIC COMBINATORICS

Two following courses that go hand in hand are by Prof Robert Sedgewick.

Analysis of Algorithms , Review of the course

Analytic Combinatorics , Review of the course

The Analysis of Algorithms may seem like a CS class but is actually a math class. Both the courses are offered as Analytic Combinatorics in Princeton with Analysis of Algorithms as part 1 of the course.

Also Game Theory 1 is pre-requisite mentioned in RFC #24.

One review of Analysis of Algorithms mentioned "This course is more about mathematic than algorithms, it teaches how to solve tricky combinatorial problems"

DISCRETE OPTIMIZATION

This course is of very high quality and is great reviewed

Discrete Optimization , Review of the course

The course is for skilful programmers who know algorithms but teaches optimization technology very well.

The four above courses are bit extra than what CUPM 2015 recommend but are of very high quality and useful to both OSSU-CS students who would like to do some math classes or OSSU- Math students who would like to have applied math class oriented towards CS.

Proposal

Add courses as following

Discrete and Combinatorial Math

Applied Combinatorics is equivalent to two courses i.e, Enumerative Combinatorics and Graph Theory Courses	Duration	Effort	Prerequisites
Applied Combinatorics	16 weeks	10-12 hours/week	Introduction to Mathematical Thinking, Mathematics for Computer Science , Linear Algebra and Intro to Analysis . Also checkout Background Material for Combinatorics
Algebraic Combinatorics	8 weeks	4-5 hours/week	Mathematics for Computer Science, Intro to Abstract Algebra and Linear Algebra
Analysis of Algorithms , Textbook	9 weeks	7-8 hours/week	Intro to Comp Sci, Mathematics for Computer Science, Game Theory 1, Intro to Algorithms (or any other Algorithm class)
Analytic Combinatorics, Textbook	8 weeks	7-8 hours/week	Analysis of Algorithms
Discrete Optimization	8 weeks	12-14 hours/week	Intro to Comp Sci, Mathematics for Computer Science, Intro to Algorithms (or any other Algorithm class) and Linear Algebra

Why MIT Intro to Algorithms as pre-requisite. MIT uses Python for Intro to Algorithms which is also an important language for Data Science and Statistical Area where Applied Math students will be benefited.

End Note Where topics like Abstract Algebra, Logic and Geometry gives a perspective of pure math Probability, Statistics + Combinatorial Math gives a perspective for applied math

[aayushsinha0706]

Also I dont think it will cause problems to MATH students who would like to have a Depth study in Combinatorics but without use of Comp Sci

The courses:

Applied Combinatorics(equivalent to two courses) Algebraic Combinatorics

will be sufficient enough to cover depth study in Applied Combinatorics

[aayushsinha0706]

Closing down this issue and new issue will be made in near future for courses in Probability, Statistics and Combinatorial math.