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Irish Debbarma

Masters in Mathematics at Indian Institute of Science, Bangalore

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Courses taken

Courses taken

Mathematics

  • Real Analysis and Linear Algebra-I (3:0) taken in Aug-Dec 2019
  • Real Analysis and Linear Algebra-II (3:0) taken in Jan-April 2020
  • Probability and Statistics (3:0) taken in Aug-Dec 2020 notes (best viewed in dark mode)
  • Introduction to Basic Analysis (3:1) taken in Jan-April 2021 notes
  • Introduction to Algebraic Structures (3:1) taken in Jan-April 2021 course website
  • Ordinary Differential Equations (3:1) taken in Jan-April 2021
  • Algebra- I (3:0) taken in Aug-Dec 2021 notes
  • Multivariable calculus (3:1) taken in Aug-Dec 2021 course website notes
  • Linear Algebra (3:1) taken in Aug-Dec 2021 course website notes
  • Topology (3:1) course website notes
  • Representation Theory of Finite Groups (3:0) taken in Aug-Dec 2021 notes
  • Algebra- II (3:0) taken in Jan-April 2022
  • Complex Analysis taken in Jan-April 2022 notes
  • Measure Theory taken in Jan-April 2022 notes
  • Functional Analysis (3:0) notes
  • Coxeter Groups (3:0) tried in Jan-April 2022
  • Algebraic Number Theory (3:0) taken in Jan-April 2022
  • Commutative Algebra (3:0) taken in Aug-Dec 2022
  • Analytic Number Theory (3:0) taken in Aug-Dec 2022
  • Functional analysis (3:0)
  • Lie Algebras and its representations (3:0) taken in Aug-Dec 2022
  • Elliptic Curves taken in Jan-April 2023
  • Topics in Analytic Number Theory taken in Jan-April 2023
  • Basic Algebraic Geometry taken in Jan-April 2023
  • Algebraic Geometry I taken in Jan-April 2023
  • Introduction to Modular Forms taken in Jan-April 2023
  • Commutative Algebra taken in Aug-Dec 2023
  • Linear Algebraic Groups taken in Aug-Dec 2023
  • Topics in Number theory: Galois representations taken in Aug-Dec 2023
  • Topics in Number theory: Iwasawa Theory taken in Jan-April 2024
  • Topics in Number theory: p-adic L-functions taken in Jan-April 2024
  • Introduction to Homological Algebra taken in Jan-April 2024

I have made notes which cover Algebraic Geometry, Modular forms, elliptic curves, commutative algebra, representation theory and algebraic number theory. Find it here I will complete it someday.

Physics

  • Introductory Physics-I [Mechanics, Oscillations and Waves] (2:1) taken in Aug-Dec 2019
  • Introductory Physics-II [Electricity, Magnetism and Optics] (2:1) taken in Jan-April 2020
  • Introductory Physics-III [Thermal and Modern Physics] (2:1) taken in Aug-Dec 2020

Chemistry

  • Physical Principles in Chemistry (2:1) taken in Aug-Dec 2019
  • Basic Inorganic Chemistry (2:1) taken in Jan-April 2020
  • Basic Organic Chemistry (2:1) taken in Aug-Dec 2020 notes-1 notes-2 notes-3 (best viewed in dark mode)

Biology

  • Introductory Biology I [Organismal biology and molecular basis of life] (2:0) taken in Aug-Dec 2019
  • Introductory Biology-II [Microbiology, Cell Biology and Genetics] (2:1) taken in Jan-April 2020
  • Introductory Biology-III [Molecular Biology, Immunology and Neurobiology] (2:1) taken in Aug-Dec 2020

Engineering

  • Algorithms and Programming (2:1) taken in Aug-Dec 2019
  • Introduction to Electrical and Electronics Engineering (2:1) taken in Jan-April 2020
  • Introduction to Earth and Environment (2:0) taken in Aug-Dec 2020
  • Introduction to Materials Science (2:0) taken in Aug-Dec 2020
  • Introduction to Solid Mechanics (3:0) taken in Jan-April 2021 notes
  • Game Theory (3:1) taking in Jan-April 2022
  • Computational Complexity Theory taken in Aug-Dec 2022

Useful Resources

If you do not enjoy learning then are you even learning.

Youtube channels:

The following is list of channels that do slightly more advanced stuff:

Webpages

Besides these, there are multiple discord servers where people are actively studying. Joining few of them could also be useful.

If you wondered how do people typeset those beautiful math papers and books, the answer is LaTeX. An essential tool (not necessary) which will come in handy a lot. You can learn it from here and of course google. (Thumb rule: if you want a certain command most likely it is \command, eg: \since, \therefore) Another essential tool that comes in handy for mathematicians is sagemath which you can learn here.

Recommendations

Maths

  1. Real Analysis
    • Tom Apostol. Calculus Volume - I, II
    • Ghorpade, Limaye. A course in Calculus and Real Analysis
    • Ghorpade, Limaye. A course in Multivariable Calclulus and Analysis
    • Walter Rudin. Principle of Mathematical Analysis
    • Abbott. Understanding Analysis
    • Rami Shakarchi. Problems and Solutions for Undergraduate Analysis
    • Terence Tao. Analysis I, II
      Apostol volumes and/or Ghorpade, Limaye volumes can be used as beginner text. Rudin’s book is a classic but might not be very suitable for people who are seeing analysis for the first time.
  2. Abstract Algebra
    • Joseph Gallian. Contemporary Abstract Algebra
    • Dummit and Foote. Abstract Algebra
    • Serge Lang. Undergraduate Algebra
    • Serge Lang. Algebra Gallian would be a nice place to start your journey. Once you are done you can move to Dummit Foote (it covers almost everything) and after that if you continue you will be using books that are dedicated to certain topics anyway. Lang’s Undergraduate Algebra can also be a nice first time source.
  3. Combinatorics
    • Aigner. A course in enumeration
    • Andreescu, Feng. A Path to Combinatorics for Undergrduates
    • R.P. Stanley. Enumerative Combinatorics
      Aigner’s book is a very nice one and can be used independent of others. Otherwise all three of them are very nice.
  4. Basic Number Theory
    • D.M. Burton. Elementary Number Theory
    • Niven, Montgomery. Introduction to Theory of Numbers
      Burton’s book is a classic and should be the book for beginners. Once you are comfortable with the stuff in Burton you can move to Niven.
  5. Topology
    • Munkres. Topology
    • M.A. Armstrong. Basic Topology
    • Sidney A. Morris. Topology without tears (available online for free) [//]: # ( )
  6. Linear ALgebra
    • Gilbert Strang. Linear Algebra and its applications
    • Hoffman, Kunze. Linear Algebra
    • Sheldon Axler. Linear Algebra done right
      All three books are excellent. Use whatever you like.
  7. Analytic Number Theory
    • Tom Apostol. Introduction to Analytic Number Theory
    • Davenport. Multiplicative Number Theory
  8. Complex Analysis
    • Bak, Newman, Complex Analysis
    • Conway. Functions of One Complex Variable
    • Ahlfors. Complex Analysis
    • Shakarchi. Problems and solutions for Complex Analysis
  9. Measure Theory
    • Gail S. Nelson. A User-Friendly Introduction to Lebesgue Measure and Integration
    • Stein, Shakarchi. Real Analysis-Measure theory, integration and Hilbert Spaces
    • Sheldon Axler. Measure, Integration and Real Analysis
    • Royden. Real Analysis
    • Folland. Real Analysis
  10. Functional Analysis
    • Conway. A course in functional analysis
  11. Algebraic Number Theory
    • Daniel Marcus. Number Fields
    • Frazer Jarvis. Algebraic Number Theory
    • R.A. Mollin Algebraic Number Theory
    • Robert Ash. A Course in Algebraic Number Theory
    • M. Ram Murty, Jody Esmonde. Problems in Algebraic Number Theory
    • Serre. A course in arithmetic
  12. Representation Theory of finite groups
    • Etingof’s notes
    • Serre. Linear Representations of finite groups
    • Fulton, Harris. Representation Theory, A first course
  13. Commutative Algebra
    • Atiyah. Introduction to commutative algebra
    • Eisenbud. Introduction to Commutative Algebra with a view towards algebraic geometry
  14. Field and Galois Theory
    • Howie. Fields and Galois Theory
    • James Milne. Fields and Galois Theory
    • Tom Leinster. Galois Theory (available online for free)
  15. p-adic numbers and Cyclotomic fields
    • Neal Koblitz. p-adic numbers, p-adic analysis, and Zeta functions
    • Lawrence C. Washington. Introduction to Cyclotomic fields
  16. Modular forms
    • Diamond, Shurman. A first course in modular forms
    • Serge Lang. Introduction to modular forms
    • Tom M. Apostol. Modular functions and Dirichlet series in Number Theory
    • Problems in the theory of modular forms
  17. Coxeter Groups
    • Humphreys. Reflection groups and coxeter groups
    • Anders Bjoner, Francesco Brenti. Combinatorics of Coxeter Groups
  18. Lie Groups, Lie Algebras and representations
    • Humphreys. Introduction to lie algebras and representation theory
    • Roger Carter. Lie algebras of finite and affine type
    • Anthony Henderson. Representations of Lie Algebras. An introduction to $\mathfrak{gl}{n}$ _
    • B.C. Hall. Lie Groups, Lie Algebras and representations- An elementary introduction
    • Sepanski. Compact Lie Groups
  19. Tate thesis
    • Deitmar. A first course in harmonic analysis
    • Deitmar, Seigfried. Principles of harmonic analysis
    • Dinakar Ramakrishnan, Valenza. Fourier Analysis on Number Fields
    • Cassels, Frohlich. Algebraic Number theory
    • Chandrashekharan. A course on topological groups
    • Ribes, Zalesskii. Profinite Groups
    • Bjorn Poonen notes. Tate’s thesis (available online)
  20. Analytic Number Theory
    • Tom M. Apostol. Introduction to Analytic Number Theory
    • Davenport. Multiplicative Number Theory
    • Serre. A course in arithmetic
  21. Sieve theory
    • ALINA CARMEN COJOCARU, M. RAM MURTY. An Introduction to Sieve Methods and Their Applications
  22. Automorphic Forms
    • Deitmar. Automorphic Forms
    • Borel, Casselman. Automorphic Forms, representations and L-functions. Part-1,2
    • Bump. Automorphic Forms and representations
  23. Galois representations
  24. Category theory/Homological Algebra
    • Rotman. An introduction to homological algebra
    • Simmons. An introduction to category theory
    • Steven Roman. An introduction to the language of category theory
    • Lawvere, Schanuel. A first introduction to categories My personal favourite is the book by Lawvere, Schanuel. Although, I must admit that I picked up a lot of category theory as and when needed and not all of it at one go. I also benefitted a lot from Borcherds youtube channel. Now, I go back to Rotman whenever I need to refer to something.

General

  1. Simon Singh. Fermat’s Last Theorem
  2. The Music of Primes