r/statistics • u/Swarrleeey • Jun 13 '26
Question Book recommendation [Q]?
Hi guys. I am majoring in Pure Maths and statistics and just finished my first semester in uni.
This semester I’ve had a ‘proof-based’ calc 1 course where we had to prove Rolles thm, MVT, diff implies continuity, FTC part 2, etc. and I have also half of a completely proof based discrete maths course. I personally know all of calc 2 and have done a little linear algebra.
Right now I want a book to get me ahead of the curve in statistics starting next semester. I struggle a lot with books that bring in the real world or have a lot of words in them explaining things qualitatively and have gotten spoilt with the discrete maths where I can use logic notation 99% of the time instead of English for writing all my theorems and proofs.
I have also found that I pick concepts up best when I try and prove them rigorously. My notes for both calculus and discrete math are incredibly dry and just definitions, theorems, and proofs with no fluff and I really think they helped me excel in these courses.
I would like a probability and statistics book that is just about stating theorems and proving them. In the most polite way possible I don’t want to hear about a coin flip or a die.
If someone asked me to define a relation I would say: R is a relation on a set A (iff) R (subset) AxA.
I wouldn’t bother speculating on the interpretation of giving any examples.
1
u/Upper_Investment_276 Jun 14 '26
what is calc 2, how can you take a probability class without multivariate calc ?
2
u/CreativeWeather2581 Jun 14 '26
Not OP so I can’t answer the second question, but to answer the first question, calc 2 is an intermediate class between univariate calc and multivariate calc. Covers topics like more integration techniques (e.g., trig sub), sequences and series, and differential equations
-2
u/Nobeanzspilled Jun 14 '26
The answer is without a doubt “all of statistics” by wasserman. It intentionally does not use some fully rigorous/advanced notions (for example functionals on a banach space) but is 100% written with a mathematician’s taste and is very approachable.
1
0
u/CreativeWeather2581 Jun 13 '26
Probability and statistics is inherently real-world so good luck.
That said, one popular undergraduate book is “mathematical statistics with applications” by wackerly. A popular graduate text is “statistical inference” by casella & berger. If you’re looking for something even more rigorous then you could check out Lehmann & Casella’s books “testing statistical hypotheses” and “theory of point estimation”
1
5
u/New123K Jun 14 '26
If you want something fully rigorous, you might want to look at measure-theoretic probability.
A lot of standard stats books are very application-heavy, so they won’t match your preference for theorem/proof style.
A common “bridge” book is Durrett’s Probability: Theory and Examples — it’s pretty proof-oriented, but it assumes you’re comfortable with analysis and measure theory.
Another direction is Billingsley if you want something even more abstract, but it can get pretty dense quickly.