• 📘 Vector Spaces
• 📘 Linear Independence and Dependence, Basis and Dimension
• 📘 Eigenvalues and Eigenvectors
• 📘 Linear Transformations
• 📘 Diagonalisable and Jordan Blocks
• 📘 Inner Product Spaces and Quadratic Forms
• 📘 Dual Spaces and Operators

Analysis

• Real Analysis – S. Kumaresan
• Topology of Metric Spaces – S. Kumaresan
• Metric Spaces – P. K. Jain, Khalil Ahmad
• Real Analysis, Carothers –link

Against the common notion, "Rudin, Bartle-Shebert, Apostol" aren't of much use. Working with them is like admiring a masterpiece from a distance. To get closer and make your hands dirty, go out with books of average and amazing problems.

One would refer to the expository articles of Dr. S. Kumaresan:

• MTTS Articles
• Kumaresan Books

Algebra

• Contemporary Abstract Algebra – J.A Gallian
• Abstract Algebra – Frank Ayres link
• Abstract Algebra – Gregory T Lee link
• Abstract Algebra – Khanna & Bhambri link

Same here — "Herstein, Dummit-Foote" are masterpieces for Modern Algebra, but make your hands dirty with Frank Ayres. Alongside, one can make use of video lectures like Benedict Gross (YouTube).

Linear Algebra

• Linear Algebra Done Right – Sheldon Axler link
• Linear Algebra – Lipson & Lipschutz – Schaum Problem Outlines
• Linear Algebra, A Geometric Approach – S. Kumaresan link

Complex Analysis

• Complex Variables Demystified – McMahon link
• Visual Complex Analysis – Needham (link)
• Complex Variables – HS Khasana link
• Complex Variables – Spiegel & Lipschutz – Schaum Outlines
• Intro to Complex Analysis – P. Duraipandian

Topology

• Topology Without Tears – SA Morris link
• Topology – J.R. Munkres
• Full Notes on Topology – link
• Notes on Topology: Prof. Veeramani (NPTEL) – link

ODE & PDE

• Differential Equations – Bronson – Schaum Outlines link
• Differential Equations – M.D. Raisinghania
• An Elementary Course on PDE – Amarnath (PDF)

To be honest, haven’t referred too many books for differential equations — hope this section gets updated in the future.

Functional Analysis

• Intro to Functional Analysis and Applications – Kriezig link
• Functional Analysis – B.V. Limaye

These two are the most common books in Functional — good ones but too long. After reading Functional, one could go through this article and book by Prof. S. Kumaresan. link

Highly suggested to refer to the articles and books of Dr. Kesavan, IMSc on applying Functional Analysis to Sobolev Space (PDE) — link

Measure Theory

• Measure and Integration – Inder K. Rana | Math4All Notes1 / Notes2

P.S: I highly appreciate this channel because of the work done for math aspirants: pkalika.in | Resource File

• Complete Grad Math Syllabus
• Notes for Competitive Exams

Platforms to be familiar with

Github | Kaggle Notebooks | Geeks for Geeks | KDNuggets Blog | GateOverflow

Articles and Newsletters from kdnuggets.com are great resources to stay updated in Data Science and AI.

• Cheat Sheet for Complete Data Science (including Statistics & Math) — PDF (Link)
• Complete Cheat Sheet for ML — PDF (Link2) (great!)
• Excellent Materials for GATE DA — link

• Machine Learning for Beginners: An excellent resource that breaks down machine learning concepts clearly.
• Supervised vs. Unsupervised Learning: Key Differences explained with visuals.
• 7 Machine Learning Algorithms Every Data Scientist Should Know

Course: Intro to Machine Learning / Data Science Materials

• Python Intro — Workshop using Google Colab
• Visualize Neural Networks using TensorFlow Playground

📚 Books for References

• Stochastic Calculus for Finance - Syllabus
• Stochastic calculus for finance (two volumes), Steven Shreve, C Mellon — PDF
• Monte Carlo Methods in Engineering, Glasserman, Columbia Business School — PDF
• Options, Futures and other derivatives by John Hull — link
• Stochastic Differential Equations by Øksendal (not for beginners) — link

📰 Articles

• Kaggle Notebook: Stochastic Process
• Stamatics IITK — Finance and Stochastic Process Project
• Financial Models / Gitcode
• Quant Finance Cheat Sheet (PDF)
• Math Finance Cheat Sheet (PDF)
• Quant Finance Overview (must look)

💻 Softwares and Websites

• TradingView, GoChart, Investopedia Simulator
• Bonds: Fixed Income by Tipson
• Futures and Options (FNO) — Grow, Zerodha (India)

📘 Beginners to Read

• What is Financial Mathematics? Courses, Books, and History
• Suggested Readings by Prof. A. Goswami (IISER Pune)
• First Step to Math Finance (Read This)
• Career Guide: Certificate of Quantitative Finance (CQF)

🏛️ Finance Courses and Universities

link

📂 My Projects and Git Resources

• My complete content and project: Git Gist
• Finance in ML (Git Repo): Great Python Notebooks Git Gist

• Mathematical blog: almostsuremath.com by George Lowther

• Complete Probability course (link) by Hossein Pishro-Nik

• Elementary books
  • Basic Stochastic Processes: A Course Through Exercises, Springer
  • Introduction to Probability by Bertsekas & Tsitsiklis
  • Stochastic Calculus Teach materials

• Notes for Reference
  • Probability and Statistics - Cheat Sheet
  • Statistics - Cheat Sheet
  • Excellent Lecture Notes: Note 1 | Note 2

• Ito's Integration - Link
• Random Walks - MIT Link
• Ito's Process / Linkedin - Report

• Research tools Litmaps or Research Rabbit (Journal Seeker) ,Overleaf (LaTeX editor), LyX (Word editor), Chatpdf or Pdfdrive , Paperpal(paid) , Hypernotes or Notion , Enago plagiriazer , Mendeley & Mendeley Data.

• Numerical & Scientific Computing, MaTLAB online is the best.

• Probability & Statistics, R - Posit Cloud is much better than others .

• Python + VS Code + GitHub Google Colab ( jupyter notebooks), VS Code online , Codespaces in Git.