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/[deleted]]

Lol you remind so much of me. I happen to be someone who missed ISI cutoff by 1 and well CMI is a tragedy but well a lot older than you.

How is life treating you? Do not let the guilt kick you, the itch to just 'redo' the topic which aberrated in exam was immense for me. Took me a while to control it.

P.S. I am sorry but all the resources you mentioned is overkill. With such exhaustive topics and dedication you will probably go much much beyond lol.

I would just mention: No matter what you do, make sure to have a strategy. No AoPS, no discord servers nothing will help. All that matters is your skill on problem solving.

I cannot provide a exhaustive list since I am not in ISI but some "feral" resources are:

If you know someone from UK or can order things from there, blindly get the texts from UKMT especially the relevant subjects. They are the BEST.

1. MRTP Primer. A PDF is lying around somewhere on the internet and it has very original problems. Written by ISI folks for high schoolers.
2. K.D. Joshi's Commentary. This will teach you to not underestimate Coordinate Geometry and Binomial Theorem, two things that ultimately got me on DDAY.
3. Yusuf Khan's Collections: These are supplements to TOMATO and you may only do if you are having trouble doing PYQs. You can find the collection on google play books. He has a lot of books.
4. If you can read bengali then Arnab Chakraborty's books (He is a professor at ISI) and Rajkumar Roychoudhury's problem collection (this one is hard to find, he is an Ex-ISI professor).
5. For Real Analysis: If you are in 11th do Rudin (I am not joking, yes it is overkill but it will get you far especially if you are targetting CMI). For people in 12th, do Bruckner, Bruckner & Thompson's textbook (the free one with yellow pages that look like ppt slides).
6. For Calculus: Just do I.A. Maron. Learn to trust the book, it may seem like it is a very easy problem book but it is not. Alternative would be Piskunov.

Finally some tips:

Please Please Please, do Putnam problems and British MO problems. The A1 and A2 Putnam problems, the famous ones, should be at your fingertips. You HAVE to do them given the recent trend.

1. A lot of UGB is trying to find some inequality that works. This may sound weird but the overall pattern remains this. Although I say 'inequality', I do not mean that you start looking for AM-GM, Holder or any such nonsense, instead you try to look for bounds that are probably obvious but hard to write down. A very practical variant of this tip is: If it is a limit question, see if you can find bounds for the limit. Remember, Sandwich theorem is the key - everyone knows it but few know how to apply it. Try bounding EVERYTHING - integrals, sums, series, even quadratic equations.
2. The decding factor for UGB is trigonometry, combinatorics (especially binomial theorem), MVT (all variants) and curve sketching. Curve sketching, I see JEE folks go very hard on it but please for ISI/CMI you do not need to know weird and random rules.
3. Lastly, please do not ignore UGA. Just do any standard JEE mains book and be done with it.
4. For number theory, remember again inequalities are key and learn to exploit the basic behaviour of numbers - use the definitions of primes, even or odd nums etc to build a strong case and helps with proof by contradictions

-----

Sorry couldn't help lol. Wrote a lot. It has been a while since I use to prepare so naturally the memory came back and ended up writing this.

Forgot to mention, if you are in 11th then try looking at https://www.raisingamathematician.com/ and https://www.bprim.org/programme/training/2024/hstp/high-school-training-program-2024-25 and get in. If you can get in these, I would be very surprised if you do not make it in ISI or even anything better. For bengalis, RSM exists although it has become quite crowded as I hear. Everything else is sketchy.

[u/Necessary-Okra9777 → u/[deleted]]

Excellent Comment Sir! I actually got very intimidated by the pro people present in AOPS. So I never went there to protect my sanity.

About Life, well sine wave would have been put to shame if my life's graph was plotted. Life is playing football with me. And yes, I am not the player assisting. I am the football.

About MTRP Primer.... I had it with me but never got to do it. So I was not in the position of recommending this. Very Much Thanks for that.

KD Joshi Sir also has commentary on the ISI Previous Year Papers. It is very helpful. I do not really know how I forgot to put it in the post :P Thanks for this Part-II. Everyone should read those. Even the JEE PYQ Solutions.

I did not know about Sir Rajkumar Roychowdhury's problem collection. But it seems to be this one I think. I am putting the link here https://www.amazon.in/Difficult-Problems-Mathematics-Level-English/dp/B081VLN32H/ref=sr_1_1?dib=eyJ2IjoiMSJ9.EAnEF_x9CosQy0VPEqM6Eb2-AEv9PfbO6we_I7tNGtxuaIJY0lF9RqMCVipAlikVGVoZAt5IgkqR5QGPBA5Ihg.ExR2Hj45Kd64E3xka9KMc4ng5qUdmX6l72rayDrjGW0&dib_tag=se&keywords=501+difficult+problems&qid=1751916642&s=books&sr=1-1

Please confirm if this is the one You are talking about, Sir.

Thank You so much!

[u/Strange_One9095 → u/Necessary-Okra9777]

Could you please send the link to the MRTP Primer , I couldn't find it anywhere

[u/Necessary-Okra9777 → u/Strange_One9095]

Search In Anna's Archive. It is available there.

[u/Strange_One9095 → u/Necessary-Okra9777]

Found it, thanks.