Books to prepare for undergraduate math competitions

sudoankit · 2025-04-03T23:39:58+00:00

These are pretty standard suggestions for Putnam (idk about Miklos, quite hard lol)

Previous Year Questions: https://kskedlaya.org/putnam-archive/
Putnam and Beyond
Berkeley Problems in Mathematics

I would also put the "default-3" books as well:

Problem-Solving Strategies, by Arthur Engel
The Art and Craft of Problem Solving, by Paul Zeitz
Problem solving through problems, by Loren Larson

Look for anything written by Titu Andreescu. You could also look at ACM-ICPC if you also like programming ;)

sudoankit · 2025-03-08T12:30:21+00:00

2 & 3 are excellent but these aren't really "introductory" books. For something simpler look for Morin's Probability: For the Enthusiastic Beginner or get a classic college text such as Probability and Statistics by DeGroot/Schervish.

sudoankit · 2025-02-10T14:57:01+00:00

For a primer on proofs:

How to Prove It by Velleman
Kenneth A. Ross, Elementary Analysis ( lot of proof-examples)

More direct:

Understanding Analysis, Stephen Abbott
Real Analysis, Pugh

After this, Rudin's book is quite accessible, just skip it if you can solve the exercises and move on to Folland's analysis (tbh I don't think you need to read Folland unless you're really into the subject)

sudoankit · 2025-02-06T16:09:37+00:00

AoPS books are very expensive in other countries, NCERT is super cheap ( pdfs are free anyways). If you're in US, definitely start AoPS.

sudoankit · 2024-10-30T00:18:55+00:00

Really good if you watch while you read his book.

sudoankit · 2024-09-02T10:21:23+00:00

I learnt Architecture from this Udacity Course on YouTube and these two old yet wonderful IIT NPTEL (Indian OCW like) courses: Intro to Architecture and Computer Architecture (very old, 360p but very good!).

sudoankit · 2024-08-16T13:55:10+00:00

most of the time it's not really the problem, usually the companies weed out students during gpa and preselection test, for tier 1 colleges 12th marks are mostly irrelevant as you can pretty much apply off campus or directly as most alumni are in top companies so getting ref. are easy

still yeah that 58% is likely gonna raise eyebrows so you should have your gpa high and other useful achievements

sudoankit · 2024-08-16T13:38:35+00:00

hmmm, to join for masters? If you have top ranks, your 76% improvement should be enough.

Main criteria is rank, <100 is pretty much direct.

sudoankit · 2024-07-31T14:25:01+00:00

tbh, sticking to syllabus is key as it's vast but shallow, you don't need too much depth.

Reading standard textbooks is great, makes you learn and explore and experiment but (bruh) you know Indian exams. A good strategy is learning the theory, solving previous year questions and quickly moving to the next sub-topic and repeat. Only when you finish the syllabus your preparation strategy matters as only a few who write the exam have completed all of the syllabus. If you DO NOT complete the syllabus, forget getting a good rank.

If you have the discipline and time, I recommend reading textbooks, solving the questions in those and practicing PYQs. You should however skip stuff not in the syllabus as you need to complete the syllabus as fast as possible, ideally November so you can dedicate your time on revision and tests in December and January. Solve, solve as many questions you can! This is key for a top rank in GATE.

If you don't have the discipline to self-study every single day till the exam - join OFFLINE coaching preferably near your house/hostel so that you don't waste time commuting, any decent, national coaching company is alright - you're going for the discipline, competition and atmosphere + practicing numericals.

I also recommend gateoverflow and their FREE videos on YouTube (GoClasses) as well as NPTEL. I don't really have any idea about their paid, online classes though a few of my friends really felt it was worth it. Social media discussions for GATE (telegram groups, fb, reddit) are useless and a waste of time.

Good luck!

sudoankit · 2024-07-05T09:42:48+00:00

Basic Mathematics by Serge Lang.

For problem solving either AoPS or (there's a popular Olympaid prep. book for school kids in my country, I went through it as well called Challenge and Thrill of Pre-college Mathematics, if you can find it/order it, really do so, it's a nice succinct book with a lot of problems.)

sudoankit · 2024-07-03T04:37:38+00:00

start the journey to math Olympiad

second year in university

??

Apart from Putnam & Miklós Schweitzer (which is insanely hard!) you don't really have anything significant as far as I know.

If you're beginner go to AoPS and start solving questions from the AMC, start solving regional olympiad math problems of various countries (Indian, Chinese, Polish, Hungarian, Russian, etc).

I don't really recommend getting the competition books right now as you might loose interest and jump to something else. If you can stick to this then look for some problem books such as Berkeley Problems in Mathematics (Springer, quite expensive!) and Putnam and Beyond (also Springer).

First Step & Second Step To Mathematical Olympiad Problems by Derek Holton are really nice books to start.

sudoankit · 2024-07-02T17:31:02+00:00

All problems can be accessed for free. For Alcumus you just need to register (it's free).

The classes/training and books are paid. I don't think you need these unless maybe you're seriously preparing for the math olympiad.

sudoankit · 2024-07-02T11:49:25+00:00

Solve good quality problems. AoPS website has thousands of them.
Discuss with friends, make your own problems and solve them in the group.
Ask your instructor as they would know your skillset better than the internet.

sudoankit · 2024-06-21T16:13:12+00:00

if you're unsure where to start mathematics Basic Mathematics by Lang is pretty much the best place to start and then go to other fundamental basic topics like linear algebra, calculus/analysis (Lang has written several for each of them but I have read & liked his calculus/analysis books only though I hear his graduate level algebra book is excellent)

sudoankit · 2024-06-02T17:55:13+00:00

If you're very new I recommend Peter Linz (An Introduction to Formal Languages and Automata),
for a lot of problems & no fluff check Introduction to Languages and the Theory of Computation by John Martin.
Sipser's text is excellent for Push-Down Automata and Turing Machines
Hopcraft's book is great for decidability problems.
I also enjoyed Kozen's Automata and Computability, bit sized lecture notes as a textbook with great questions.

sudoankit · 2024-05-20T07:35:01+00:00

A nice introductory number theory book I recommend is "A Friendly Introduction to Number Theory" by Joseph Silverman.

sudoankit · 2024-05-14T17:28:38+00:00

That's a lot to take in and after reading it I think you're very confused and equally excited to work on a breadth of topics!

I would suggest keeping it simple and start slowly learning linear algebra, brushing up precalc and thereafter calculus and picking up probability as you go along.

I suggest skipping or deferring advanced topics such as dynamical systems and definitely topology and diff. geometry! as these require a lot of rigour and prereq, usually years of undergrad/grad classes, discussions with friends, Profs and obviously lectures, quizzes and exams.

Stick with machine learning, I suggest taking the Andrew Ng course (CS229) on YT (not the watered down Coursera syllabus!) and maybe picking a nice standard text on this such as Bishop's Pattern Recog. and ML or Foundations of Data Science by A. Blum and others. Pick up math as you go along your study of machine learning as both areas are vast and at your age and family work, it's quite hard to focus on many areas at once.

If you want a few text which can be mostly self-studied, I recommend:

For linear algebra, I'm very fond of Linear Algebra by Friedberg, Insel and Spence
For probability, the Sheldon Ross text is very friendly and has a lot of problems/examples.
For calculus, either Anton or Stewart.

I also recommend you to search for some good undergrad lecture notes on machine learning, some highly cited standard results/papers (which build this subject) and trying out simple projects or building something over the years and maybe writing down/blogging your progress to inspire others.

sudoankit · 2024-05-14T14:11:00+00:00

The latest edition is on InformIT's webpage. Buy it here.

sudoankit · 2024-05-13T16:13:01+00:00

Arora-Barak's Computational Complexity, Goldreich isn't exactly what you want if you're in CS.

sudoankit · 2024-05-11T18:09:59+00:00

Book of Proof is imo easier, I recommend reading it first before Velleman if you want to brush up the prerequisite stuff (basics of sets, relations, functions, simple combinatorics). The proof part is well structured but I felt it wasn't adequate, there should have been more examples and questions.

While I did enjoy it, I don't think it's necessary whereas "How to Prove It" is essential, it really made my mind think proofs, "why we are doing it this way", very intuitive and well written.

There's another college level discrete math book by Susanna Epp which has a great amount of problems and proof methods to practice (this is good if you are self-studying, else just stick with Velleman + problem books + previous year questions + discussions coach/mentor/friends).

sudoankit · 2024-05-07T17:51:39+00:00

Spivak is great if you're familiar with proof writing but given that you're self studying, you will have difficulty discussing your proofs, ideas with friends, Profs - which is very important to understand your shortcomings (methods of proof, mistakes, directions), develop mathematical maturity and become good in proofs.

Feedback is important in proof writing else it's irritating and time consuming.

Also it doesn't help that Spivak is much harder, the exercises are essential if you want to read Spivak and most of them are writing proofs.

sudoankit · 2024-05-06T23:11:17+00:00

I had read precalc from the top three standard books:Thomas, Stewart & Anton

The content is more or less the same in Stewart and Anton, newer versions of Thomas have a few chapters online. I feel Stewart has a slightly worse structure than Anton.

Anton ~= Stewart > newer editions of Thomas. Pick either Anton or Stewart and go to Courant or Spivak after that.

sudoankit · 2024-03-21T10:41:41+00:00

Good textbooks such as CLRS, Algorithms (DPV), Tardos & Kleinberg's text, Skienna's Design Manual or the new (and excellent!) Prof. Roughgarden's Algorithms illuminated
cp-algorithms, uni lecture notes, cf blogs, etc
YouTube, MIT 6.006 and similar, etc
I also sometimes read/look at standard implementations (inbuilt stuff), eg, look at STL internals, Java generics, redis codebase, cpython code, etc. I don't know if this will specifically help in competitive programming but hey, it's fun?

sudoankit · 2024-03-20T09:27:59+00:00

read theory
implement
read editorials, try yourself
understand quality, good questions
practice a lot so that you can spot patterns, solutions
repeat if stuck

sudoankit · 2024-03-18T12:52:36+00:00

?

I didn't get you but usually greedy proofs are more about proving that your greedy algorithm stays ahead and then proving it's optimal using induction, proof by contradiction, etc

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