Introduction to probability theory

Name: Introduction to probability theory
ISBN: 9780395046364

by Paul Gerhard Hoel · first published 1971

11mentions

7recommended by

11HN commenters

2013–2026first – last mentioned

64% recommend36% neutral

Why HN recommends it

An introductory probability text for beginners and readers brushing up on fundamentals. It offers a gentle, self-contained path into probability and appears on course lists and reading plans.

Summarised by Claude from recommending comments

Data & Statistics

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What Hacker News says

nextos · Nov 13, 2013 · Recommends

…knowledge: * How to Prove It (Velleman) * Algebra; Trigonometry; F&G; The Method of Coordinates (Gelfand) * Geometry (Kiselev) * Calculus Made Easy (Thompson) * How to Count without Counting (Niven) * Introduction to Probability Theory (Hoel) * The Little Schemer (Friedman) The proceed to more advanced texts like: * Naive Set Theory (Halmos) * Linear Algebra Done Right (Axler) * Geometry Revisited (Coxeter) * Infinitesimal Calculus…
on “How I faced my fears and learned to be good at math” ↗
jfaucett · Mar 3, 2018 · Recommends

…solutions manuals I would advise getting them as well so you can ensure you understand how every problem works. 1. Calculus 4th ed. by Smith and Minton 2. Introduction to Linear Algebra (Gilbert Strang) 3. Introduction to Probability Theory (Hoel, Port, Stone) 4. Discrete Mathematics and its applications (Rosen) 5. Introduction to Automata Theory, Languages, and Computation (Hopcroft) 6. Introduction to Algorithms (Cormen, Leiserson,…
on “Ask HN: Resources to learn math as a foundation for CS” ↗
leephillips · May 11, 2018 · Recommends

…(but if I weren't I would put Hamlet at the top) to focus: The stoic classics mentioned throughout these replies; Reinventing the Sacred; The Art of War; Descarte's Error; Free Will by Sam Harris Introduction to Probability Theory
on “Ask HN: Which books have made you introspect?” ↗
throwawaymath · Apr 9, 2019 · Recommends

…Theory A really rigorous treatment of probability is measure theoretic, but even if you haven't worked with measures before you'll need (real) analysis and linear algebra. Tackle those first. Feller's Introduction to Probability Theory is usually a good first course. If you don't like that, try Ross. For truly advanced probability theory, work through Shiryaev or Kallenberg. The other things you've asked for are a little under-specified…
on “Ask HN: Mathematicians, what textbooks are best for learning these math topics?” ↗
mrtnmcc · Sep 11, 2021 · Recommends

Introduction to Probability Theory https://www.amazon.com/Introduction-Probability-2nd-Dimitri-... Linear Algebra https://www.amazon.com/Introduction-Linear-Algebra-Gilbert-S... Convex Optimization https://www.amazon.com/Convex-Optimization-Corrections-2008-...…
on “Ask HN: How Do You Learn?” ↗
harshreality · Apr 12, 2014 · Recommends

…Exercises (AMS Chelsea) The classic probability book is Feller (2 vol), but it's absurdly priced. There's also Sidney Resnick's Probability Path and Adventures in Stochastic Processes. Grinstead & Snell - Introduction to Probability Theory is free[2], and there's also Chung's A Course in Probability Theory (Academic Press/Elsevier). Dover publishes at least three good books on counterexamples and pathological cases: Counterexamples in…
on “Ask HN: Math books like SICP?” ↗
chuckus · Dec 26, 2016 · Recommends

…own to ensure we retain and can apply the knowledge in the long term, which starts with laying a foundation of fundamentals. For brushing up on those fundamentals, I recommend Bertsekas & Tsitsiklis : Introduction to Probability. Theory supported with lots of examples, as well as comparing the theory to "intuition" and why it is much more effective to apply the theory.
on “Learning Machine Learning: A beginner's journey” ↗
graycat · Oct 2, 2015 · Mentions

…signed measure permits negative values. And of course at times want a measure that yields complex numbers. Measure theory is in, say, P. Halmos, Measure Theory. The back of Halmos has a really nice introduction to probability theory, the Kolmogorov three series theorem in stochastic processes, etc. For more in stochastic processes there is, of course, the classic J. Doob, Stochastic Processes. Halmos was a Doob student and then…
on “Foundations of probability theory” ↗
hiddencost · Mar 15, 2016 · Mentions

…couple things. (I'm assuming you're comfortable with multivariable calculus.) Andrew Ng's coursera course is good. PRML (pattern recognition and machine learning) by bishop is good, and has a useful introduction to probability theory. You also want a good grounding in linear algebra. Strang is basically the authority on linear: http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-... You want a strong grounding in probability…
on “Enrollment Is Surging in Machine Learning Classes” ↗
kercker · Nov 13, 2017 · Mentions

I find this site greatly useful. Undergraduate courses STAT 100: Statistical Concepts and Reasoning STAT 200: Elementary Statistics STAT 414: Introduction to Probability Theory STAT 415: Introduction to Mathematical Statistics STAT 461: Analysis of Variance STAT 462: Applied Regression Analysis STAT 464: Applied Nonparametric Statistics Statistical Analysis…
on “The Department of Statistics Online Learning” ↗
dtj1123 · Jul 1, 2026 · Mentions

I recently started Introduction to Probability theory by Blitzstein and it feels a lot like what you're referring to. The author introduces something called 'proof by story', where instead of just running through algebra to prove equivalence of two expressions,…
on “Mathematics: Its Content, Methods and Meaning” ↗