Name: Introduction to Probability
ISBN: 9781886529236

Introduction to Probability

An intuitive, yet precise introduction to probability theory, stochastic processes, statistical inference, and probabilistic models used in science, engineering, economics, and related fields. This is the currently used textbook for an introductory probability course at the Massachusetts Institute of Technology, attended by a large number of undergraduate and graduate students, and for a leading online class on the subject. The book covers the fundamentals of probability theory (probabilistic models, discrete and continuous random variables, multiple random variables, and limit theorems), which are typically part of a first course on the subject. It also contains a number of more advanced topics, including transforms, sums of random variables, a fairly detailed introduction to Bernoulli, Poisson, and Markov processes, Bayesian inference, and an introduction to classical statistics. The book strikes a balance between simplicity in exposition and sophistication in analytical reasoning. Some of the more mathematically rigorous analysis is explained intuitively in the main text, and then developed in detail (at the level of advanced calculus) in the numerous solved theoretical problems.

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rg111May 2022

- Linear Algebra: Gilbert Strang's book + MIT OCW video series. Alternatively/additionally Sheldon Axler's Linear Algebra Done Right. Must watch 3blue1brown series on LinAlg.

- Analysis: Spivak's Calculus (yes). Understanding Analysis is also supposed to be good.

- Probability: Introduction to Probability by Dimitri Bertsekas and John Tsitsiklis.

- Graphs: Plenty nice books. Can also choose GT specific chapters from Discrete Math books.

Edit: If you haven't have formal Math training, you need to learn how to write proofs. For Proofs, I wholeheartedly recommend Jay Cummings's book "Proof: A Long Form Text Book".

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rg111Jan 2022

I do not know how this book is, but if you are looking to learn Probability by yourself, a great resource is- Introduction to Probability by Dimitri Bertsekas and John TTsitsiklis.

I highly recommend it.

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painintheazzApr 2020

Like the others said you want to know basic linear algebra and probability. Another thing very helpful in general is mathematical analysis. From elementary real analysis up through measure theory and Lebesgue integral, at least. From here a lot of advanced math will open up to you: for example, big-boi probability theory and statistics.

Here below is an intro to how math people think (FREE):

* Book of Proof by Hammack: https://www.people.vcu.edu/~rhammack/BookOfProof/

For intro linal and probability, try

* Introduction to Probability by Bertsekas, Tsitsiklis: https://www.amazon.com/Introduction-Probability-2nd-Dimitri-...

* Linear Algebra by Kuldeep Singh: https://www.amazon.com/Linear-Algebra-Step-Kuldeep-Singh-ebo...

Both (clear and easy to read) books above are on l#ibgen, I believe. Also, there's a free online course based on Bertsekas'/Tsitsiklis' book on edx if I recall correctly.

I prefer textbooks to online stuff when it comes to math (especially analysis). The many elementary analysis books that I know (and like) are print-only.

Although, you could probably do the following one after the other:

For pre-analysis, try

* From Calculus to Analysis by Schinazi: https://www.google.com/books/edition/From_Calculus_to_Analys...

For modern analysis, try

* Measure, Integration and Real Analysis by Axler: https://link.springer.com/content/pdf/10.1007%2F978-3-030-33...

The one by Schinazi is on l#ibgen and the one by Axler is available free.

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mhneuJul 2018

If you're working through Spivek and Apostol, get Feller v1 and v2. Same level of rigor and emphasis on intuition. (If you're having fun after that, pick up Gallager's book on stochastic processes. Similar approaches, intuition, and focus on discrete probability to skip the metric theory complications of continuous dists.)

Another very good book is Bertsekas and Tsitsiklas, Introduction to Probability. This book will also give you some intuition.

I've heard Grimmitt recommended but I think B&T is better.

You could also start with Papoulis (a stochastic processes classic book, but it does the intro probability too.)

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yogeshpJul 2018

Introduction to Probability, 2nd Edition by Dimitri P. Bertsekas, John N. Tsitsiklis. It is textbook for EECS Probability course at MIT and very well written for beginners.

Additionally, there are video lectures available on MIT OCW which mirror this book closely.

https://www.amazon.com/Introduction-Probability-2nd-Dimitri-...

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shortoncashAug 2015

Get "Introduction to Probability" by Dmitri Bertsekas. The solutions are available on the web also, so it makes it easy to work through the problems until you get it.

There's other good books out there, but I still keep the Bertsekas book on my desk, along with Kutner's Applied Linear Regression Models.

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