Introduction to Probability

What Hacker News says

1. sudoankitOct 2023
   I particularly like Statistical Inference by George Casella and Roger Lee Berger.

   You could also look at Introduction to Probability by Joseph K. Blitzstein and Jessica Hwang (available for free here: http://probabilitybook.net (redirects to drive)).

   thread
2. photon_linesMay 2022
   Great introductory books along with videos:

     - Mathematics and Its History (John Stillwell)
     - Journey through Genius: The Great Theorems of Mathematics (William Dunham)
     - Proofs Without Words: Exercises in Visual Thinking (Roger B. Nelsen)
     - The Mathematical Universe: An Alphabetical Journey Through the Great Proofs, Problems, and Personalities (William Dunham)
     - Odds & Ends: Introducing Probability & Decision with a Visual Emphasis (Jonathan Weisberg)
     - Introduction to Probability (Joseph K. Blitzstein, Jessica Hwang)
     - The Secret Life of Equations: The 50 Greatest Equations and How They Work (Richard Cochrane)
     - Euler's Gem: The Polyhedron Formula and the Birth of Topology (David S. Richeson)
     - 3Blue1Brown Essence of Linear Algebra: https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab 
     - 3Blue1Brown Differential Equations: https://www.youtube.com/playlist?list=PLZHQObOWTQDNPOjrT6KVlfJuKtYTftqH6 
     - Dynamics: The Geometry of Behavior (Ralph Abraham, Christopher Shaw)
     - Geometry, Relativity and the Fourth Dimension (Rudolf Rucker)
     - 3Blue1Brown Essence of Calculus: https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr 
     - Calculus for the Practical Man (J.E. Thompson)
     - Div, Grad, Curl, and All That: An Informal Text on Vector Calculus (Harry M. Schey)
     - Who Is Fourier? a Mathematical Adventure
     - Physics, Topology, Logic and Computation: A Rosetta Stone (John C. Baez, Mike Stay)
     - An Illustrated Guide to Relativity (Tatsu Takeuchi)
     - The Mathematics Of Quantum Mechanics (Martin Laforest)
     - A Student's Guide to Maxwell's Equations (Daniel Fleisch) or if you're also interested in a visual guide, I wrote one as well: https://github.com/photonlines/Intuitive-Guide-to-Maxwells-Equations 
     - Introduction to Elementary Particles (David J. Griffiths)
     - An Invitation to Applied Category Theory: Seven Sketches in Compositionality (Brendan Fong, David I Spivak)
     - Solving Mathematical Problems: A Personal Perspective (Terence Tao)

   Show morethread
3. s1t5Mar 2020
   Harvard's Stat110 by Joseph Blitzstein and the accompanying book Introduction to Probability - https://projects.iq.harvard.edu/stat110/youtube
   thread
4. pedrodelfinoNov 2018
   I recommend "Introduction to Probability" by Joseph K Blitzstein and Jessica Hwang.

   This book is tough. Really tough. However, you are really going to do "deliberate practice" while having a go on the assignments.

   It bothers me that the author does not provide the answer to most of the questions. This is specially bad in this field of Mathematics (Probability). As an example, in calculus you can always plot the curve, the derivative and see if the result makes sense, in probability theory it is hard to have a simple and safe sanity check.

   You can watch all classes from Harvard here for free: https://www.youtube.com/watch?v=KbB0FjPg0mw&list=PL2SOU6wwxB...

   If you want, there is also a MOOC in EdX with the same material: https://www.edx.org/course/introduction-to-probability-0

   Sheldon Ross' book is also a good one. It was mentioned here. I specially like the section on theoritical problems, only with exercises on proofs. Every chapter has one. However, Joe Blitzstein problems are more challenging and will train you more on intuition.

   Show morethread
5. adamnemecekNov 2016
   To be honest, this isn't the best list, it's a bit too blog heavy. I've started reading up on ML only recently but here are my recommendations. Note that I haven't went through all of them in entirety but they all seem useful. Note that a lot of them overlap to a large degree and that this list is more of a "choose your own adventure" than "you have to read all of these".

   Reqs:

   * Metacademy (http://metacademy.org) If you just want to check out what ML is about this is the best site.

   * Better Explained (https://betterexplained.com/) if you need to brush up on some of the math

   * Introduction to Probability (https://smile.amazon.com/Introduction-Probability-Chapman-St...)

   * Stanford EE263: Introduction to Linear Dynamical Systems (http://ee263.stanford.edu/)

   Beginner:

   * Andrew Ng's class (http://cs229.stanford.edu)

   * Python Machine Learning (https://smile.amazon.com/Python-Machine-Learning-Sebastian-R...)

   * An Introduction to Statistical Learning (https://smile.amazon.com/Introduction-Statistical-Learning-A...)

   Intermediate:

   * Pattern Recognition and Machine Learning (https://smile.amazon.com/Pattern-Recognition-Learning-Inform...)

   * Machine Learning: A Probabilistic Perspective (https://smile.amazon.com/Machine-Learning-Probabilistic-Pers...)

   * All of Statistics: A Concise Course in Statistical Inference (https://smile.amazon.com/gp/product/0387402721/)

   * Elements of Statistical Learning: Data Mining, Inference, and Prediction (https://smile.amazon.com/gp/product/0387848576(

   * Stanford CS131 Computer vision (http://vision.stanford.edu/teaching/cs131_fall1617/)

   * Stanford CS231n Convolutional Neural Networks for Visual Recognition (http://cs231n.github.io/)

   * Convex Optimization (https://smile.amazon.com/Convex-Optimization-Stephen-Boyd/dp...)

   * Deep Learning (http://www.deeplearningbook.org/ or https://smile.amazon.com/Deep-Learning-Adaptive-Computation-...)

   * Neural Networks and Deep Learning (http://neuralnetworksanddeeplearning.com/)

   Advanced:

   * Probabilistic Graphical Models: Principles and Techniques (https://smile.amazon.com/Probabilistic-Graphical-Models-Prin...)

   I have also found that looking into probabilistic programming is helpful too. These resources are pretty good:

   * The Design and Implementation of Probabilistic Programming Languages (http://dippl.org)

   * Practical Probabilistic Programming (https://smile.amazon.com/Practical-Probabilistic-Programming...)

   The currently most popular ML frameworks are scikit-learn, Tensorflow, Theano and Keras.

   Show morethread
6. adamnemecekOct 2016
   "Introduction to probability" is amazing. It really set the bar for what an academic book could be https://www.amazon.com/Introduction-Probability-Chapman-Stat...
   thread