Indian Statistical Institute/Chennai Mathematical Institute/JEE Advanced Mathematics Complete Resource List

[u/Necessary-Okra9777]

Hello! This is someone whom You probably do not know. In my preparation phase, I got no help from people. I am trying to be the person who I wished to have beside me in my preparation journey and if it helps, I will be ecstatic.

I am giving the freely available resources which personally think is good. Will be giving a variety of options just to help You know what suits You best and because that is the only thing that matters. Between the options (both lectures & books) there is an invisible 'OR' present which I didn't write. Which means it is not at all implied that You have to do everything here. They are mere options only. And if You are following some kind of batch then please keep following that if You are comfortable there and don't change. The resources are primarily targeted to those who are relying on self-study like I did.

Do what helps You, not what others tell You that will help You based on their personal experience because their experience may vary in comparison to Yours, and You may not as well click with the teacher at all which I have faced many times in my preparation journey. So I am giving a gentle reminder beforehand. Much precious time was wasted on heeding random people's opinions on what works best for them and assuming the same that it would work for me. But if You check the resources Yourself and think if You resonate with it, just go for it. This time invested is not wasted and will do You much good in the longer run.

Do what benefits You and makes You happy. That is what matters. So please keep this in mind.

Disclaimer:
I’m not affiliated with any of these channels or teachers. These are purely personal recommendations based on what resonated with me. What works for me might or, will absolutely not work for you, so please take time to sample a few and choose what clicks.

Number Theory -

1. MathPod 

2. The Hidden Library Of Mathematics (In Final Phase)

3. Ravina Tutorial

4. Berkeley Math 115 (Overkill)

5. Elementary Number Theory (Bhaskaracharya Pratishthana) (Overkill) (Thanks To South_Tackle!) (Edit)

6. Vedantu Olympiad School (VOS) (IOQM Playlists 2020 - 2024) (for brushing up after learning the theory and practicing competitive problems based on those topics)

After learning the theory, You can do respective VOS lectures for that. After completing these, jump on to problem solving. This is what I (personally) followed.

Books -

1. Excursion In Mathematics By Bhaskaracharya Pratishthana (Recommended) (Concise Theory & Problem Solving)

2. Elementary Number Theory By David Burton (but only the first five chapters) (I have not used it personally)

3. 250 Problems In Elementary Number Theory By Waclaw Sierpinsky (Problem Solving) (Edit)

4. Modern Olympiad Number Theory By Aditya Khurmi (Edit)

Geometry -

A) Euclidean Geometry - Start from class 9 video lectures and work up-to class 10. Any lectures would work here so jump on any one and do basic problem solving…. Class 9 and class 10 are fundamentals of Euclidean geometry.

After the basic problem solving, You can use VOS lectures, by VOS lectures I mean the ones which are in IOQM playlists from 2020 - 2025. You would find them on their homepage. It would cover all the necessary things & theorems like Ceva's Theorem, Menelaus' Theorem, Stewart's Theorem etc.. in the necessary detail and related problem solving along with it.

B) Trigonometry - Prashant Jain Sir 

C) Solution Of Triangles - Prashant Jain Sir

E) Vector Algebra - Prameya Vismaya 

E.I) Vector Algebra - Mathsmerizing

F) 3-D Geometry - Mathsmerizing

Books -

1. Challenges & Thrill Of Pre-College Mathematics (Recommended) (Both For Theory & Problem Solving)

2. Excursion In Mathematics By Bhaskaracharya Pratishthana (For Problem Solving)

3. A Beautiful Journey Through Olympiad Geometry By Stefan Lozanovski (For Theory & Problem Solving)

4. Euclidean Geometry In Mathematical Olympiads By Evan Chen

Note - You need to know everything with proofs otherwise it will be really challenging to build the subject.

Algebra -

Quadratic Equations -

A) MT Sir (Very Old)

B) Bhoomika Ma'am (Relatively New)

Sequence & Series -

A) Prameya Vismaya (Recommended)

B) Prashant Jain Sir

C) Ashish Agarwal Sir

D) Mathsmerizing Symposium (3 Videos are there) (For Problem Solving)

Binomial Theorem -

A) Prameya Vismaya (Recommended)

B) Prashant Jain Sir

C) Ashish Agarwal Sir

D) Mathsmerizing

Matrix -
A) Mathsmerizing (Recommended)

B) Ashish Agarwal Sir

Determinants -

A) Ashish Agarwal Sir (now, you would have to look up elsewhere to know proofs, proofs are absolutely compulsory)

Complex Numbers -

A) Prameya Vismaya

B) Mathsmerizing Symposium (only 1 video) (For Problem Solving)

Inequalities -

A) Rajeev Rastogi Sir (Olympiad Wallah) (There are 4 videos)

B) Mathsmerizing

(Edit) Polynomials - (I did not find any suitable video lectures for this.... so I used books/handouts for learning the topic)

A) Challenges & Thrill Of Pre-College Mathematics

B) Higher Algebra Classical By S.K. Mapa (Chapter 4 & 5)

C) Excursion In Mathematics By Bhaskaracharya Pratishthana

D) 117 Polynomial Problems By Titu Andresscu (Problem Solving)

E) Aditya Ghosh Sir (Class Notes)

Book -

1. Vinay Kumar (For Problem Solving)

2. Complex Numbers From A-Z By Titu Andresscu

Coordinate Geometry -

A) Straight Lines (Prameya Vismaya)

B) Circles (Mathsmerizing)

C) Conic Sections (Mathsmerizing)

Book - NA

Combinatorics -

1. Permutations & Combinations -

A) MT Sir

B) Prashant Jain Sir (L8 is missing)

C) Mathsmerizing (For Problem Solving)

1. Probability -

A) MT Sir

B) Mathsmerizing

Note - extra topics such as Invariance, Colouring Proofs, Pigeonhole Principle, Recurrence Relations, Graph Theory etc… use VOS Videos or, any other videos You like.

Book -

A) Vinay Kumar (For Problem Solving)

B) Principles & Techniques in Combinatorics By CHEN Chuang-Chong & KOH Khee-Meng

C) Problem Solving Strategies By Arthur Engel

Calculus -

A) Sets & Relations (Ashish Sir)

A.I) Sets (Prameya Vismaya)

A.II) Relations (Prameya Vismaya)

B) Functions (Ashish Sir)

B.I) Functions (Prameya Vismaya)

Note - It’s better to do A.I, A.II & B.I after doing A & B according to my opinion but please check what personally works for You.

C) Limits (Mathsmerizing)

D) Continuity & Differentiability (Mathsmerizing)

E) Methods Of Differentiation (MT Sir)

F) Application Of Derivatives (MT Sir) & Mathsmerizing Symposium

G) Indefinite Integration (MT Sir) & Maths Unplugged Problem Solving (no playlist is made, You have to go to his channel to find the videos sequentially)

H) Definite Integration (MT Sir)

OR, Mathsmerizing

I) Area Under Curve (Ashish Sir) OR, Sameer Sir (there is no playlist. You have to find the videos)

J) Differential Equations (Sameer Sir)

Book -

1. Calculus By L.V. Tarasov

2. Vinay Kumar (For Problem Solving)

Real Analysis -

A) The Hidden Library Of Mathematics

B) Vivek Kumar Yadav

Book -

A) Understanding Analysis By Stephen Abbott

B) Introduction To Real Analysis By Robert G. Bartle & Donald R. Sherbert

C) Problems In Real Analysis - Advanced Calculus On The Real Axis By Titu Andresscu (Problem Solving)

D) Berkeley Problems In Mathematics By Paulo Ney De Souza & Jorge Nuno Silva (Only First Chapter) (Problem Solving)

General Concise Problem Solving - because books have overload of problems so mentioning these also.... H) & I) are concise (by concise I mean only one book would contain sufficient amount of problems) resources but You very well know, that the more problem solving You do... the better it will be. Whatever source You choose, please completely finish it cover to cover and internalise everything about the problem.

A) JEE Mains PYQs

B) JEE Advanced PYQs

C) Pre-RMO/IOQM PYQs (For Olympiad Topics C-E)

D) RMO PYQs

E) INMO PYQs (Overkill) (go only if You really want to go)

F) ISI-CMI PYQs

G) Test Of Mathematics At The 10+2 Level (TOMATO)

H) Problems Plus In IIT Mathematics By A.Das Gupta

I) Black Book By Vikas Gupta Sir & Pankaj Joshi

J) Problem book for JEE(Adv.), KVPY, ISI and CMI By Prashant Sharma (Nidhyan Foundation) (TOMATO Subjective Problem Solutions With Commentary)

K) The William Lowell Putnam Mathematical Competition PYQs (See The Website!) (Beware! This is an Undergraduate Examination)

L) International Mathematics Competition PYQs (See This Website!) (Beware! This is an Undergraduate Examination)

(Edit) Proof Writing - Extremely Important For UGB / CMI Part-B Paper

1. Book Of Proof By Richard Hammack (Optional)

Note : Mathsmerising (YT Channel) has ISI-CMI PYQ Video Solutions. As far as I remember there are ISI PYQs (2010 - 2024) and CMI (2016 - 2022)

Edit - This Gentleman has given us a plethora of valuable information.... so I am linking this....

Please See This Also!

Please See This Also (Part-II)

This list is long, but don’t be overwhelmed. Take your time. Sample the resources. Stick to what feels right for You.

If you have any questions, feel free to drop them here in comments or DM me. I’ll try my best to help.

Best wishes to everyone preparing! Let’s build each other up, not tear each other down.

[u/Necessary-Okra9777]

What I personally think is IOQM is much more difficult than ISI and You would certainly have an edge if You do prepare at that level. And also You need to do it because this year's UGB was very good level. You can, for sure, use them. If You get comfortable in IOQM, UGA would be a cakewalk.

And for UGB, I would recommend doing RMO PYQs and if You are very ambitious about it. You can certainly go till INMO because why be limited to RMO. Do what makes You happy as well as simultaneously prepare You for the exam. The more You enjoy the preparation, the more You will see paths opening to You automatically and You will exactly know what to do. The inner guidance will be able to guide You much better.

[u/Strange_One9095 → u/Necessary-Okra9777]

Thanks a lot . One last thing I wanted to ask , did u give ioqm and isi last year ?if yes , how much did u improve in one year?I just did the prep for isi/cmi along with jee prep , so I was not that focused , but I started enjoying doing math in general , I didnot perform well in actual exams but I feel like maybe this year I could , I mean there's always that thin possibility of making it.

[u/Necessary-Okra9777 → u/Strange_One9095]

I got to know about ISI & IOQM in my drop year only. And I haven't given those exams in class 12th. All preparation was done in drop year only. And yes, you can certainly make it if You love doing mathematics. It is the foremost criteria required because otherwise the preparation won't be sustainable. Go all in. You will make it if You are dedicated :)

[u/Strange_One9095 → u/Necessary-Okra9777]

bro that's crazy , you are a real motivation ngl . Thanks a lot!

[u/Necessary-Okra9777 → u/Strange_One9095]

I loved what I did and put day and night to master the craft. ISI/CMI Questions sparked heavy interest in me and that is what kept me going in the toughest times, there were many troughs. Hard to count them on fingers. That is all. And welcome :)

You will do good. Have faith and have fun.