Can you please cite a book that treats deep learning from the mathematical perspective as I tried to search, but most of the books are either technical or too superficial in terms of the mathematics behind?
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I am looking for a book that goes through the mathematical aspects of neural networks, from simple forward passage of multilayer perceptron in matrix form or differentiation of activation functions, to back propagation in CNN or RNN (to mention some of the topics).  Do you know any book that goes in depth into this theory? I've had a look at a couple (such as Pattern Recognition and Machine Learning by Bishop or Deep Learning by Goodfellow, Bengio and Courville) but still have not found a rigorous one (with exercises would be a plus). Do you have any suggestions?
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I'm starting to read Baby Rudin (Principles of mathematical analysis) now and I wonder whether you know of any companions to it. Another supplementary book would do too. I tried Silvia's notes, but I found them a bit too "logical" so to say. Are they good? What else do you recommend?
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Can someone recommend a good basic book on Geometry?  Let me be more specific on what I am looking for.  I'd like a book that starts with Euclid's definitions and postulates and goes on from there to prove thereoms about triangles, circles and other plane shapes.  I'm not interested (at this time) in a book that ties geometry in with linear algebra or explains non-euclidean geometry.  All the books I've seen seem to be of two types 1) Let us use linear algebra and other techniques to put geometry on a firm footing. Let us assume you already know Eucliean geometry and move on to more interesting stuff. These are probably too advanced for me. 2) Let us skip all that complicated postulates/proofs and make geometry fun.  Too easy.  When I was in 9th grade Honors Geometry way back in 1981/82 we had a textbook that, as I recall through my foggy memory, was very good and did systematically build up geometry from the propositions (5 of them?).  And it certainly didn't attempt to address Hilbert's contributions to geometry or explain non-Euclidean geometry. Unfortunately, I don't recall the title or author.  I suspect the book was used nationally though and for quite a number of years, so perhaps someone with a better memory than me can provide a title/author.  I do recall it had all the postulates and most major thereoms listed at the end of the book.  My motivation is two fold... 1.  Review the material myself in preparation for my advanced texts. 2.  Help my children in a few years when they take geometry.    Books I could get for the iPad/Kindle or free books (Google?) would be most appreciatied, but I'm not opposed to killing a tree either :) Thanks for all the help. Dave
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I recently took an introductory class on linear algebra (covered solving linear systems, determinants, eigenvectors, diagonalization, some vector spaces, basis and combinations, transformations etc.)   Since it was a class for engineering students, it was mostly going through the motions without any insight - felt very mechanical and repetitive. However, I want to get a deeper understanding of the material, how it relates to vector spaces, geometry etc. For this I'd like a textbook recommendation.  Keep in mind I'm just a second-year undergraduate in engineering, so something rigorous might go over my head. Thanks!
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Does the universal approximation theorem for neural networks hold for any activation function (sigmoid, ReLU, Softmax, etc...) or is it limited to sigmoid functions?   Update: As shimao points out in the comments, it doesn't hold for absolutely any function. So for which class of activation functions does it hold?
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I've taken up self-study of math. (How smart can that be?) I've just about finished a course in real analysis which spent a lot of time on metric spaces and some time revisiting calculus.  I was thinking of trying abstract algebra. I would appreciate any book recommendations.  Thanks in advance.  Andrew
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I'm a Computer Science engineer with no background in statistics or advanced math.  I'm studying the book  by Raschka and Mirjalili, but when I tried to understand the math of the Machine Learning, I wasn't able to understand the great book that a friend suggest me .  Do you know any easier statistics and math books for Machine Learning? If you don't, how should I move?
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I read single variable calculus this semester, and the course is using Thomas Calculus as the textbook. But this book is just too huge, a single chapter contains 100 exercise questions! Now I'm looking for a concise and complete textbook. I'm not interested in routine, computational exercises, but rather some challenging problem sets.  I have quite a strong basic knowledge of calculus from high school, but I still have difficulties in solving a few questions from past exam papers. So I'm looking for more challenging exercises. In fact, I'm looking forward to solving Putnam level questions.  Please suggest some textbooks with these features. Thanks in advance.
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During the next quarter at uni, I'll be taking a course in real analysis and since I prefer studying with an additional text I thought I'd come here to look for some book recommendations.  My background: I'm comfortable with linear algebra and single variable calculus, but shakey on multivariable calculus. I did have a slight introduction in to geometry.  For linear algebra I found the common recommendation of Hoffman &amp; Kunze to be very helpful (although the abstractness came as a bit of a kicker at first).   For Single variable calculus I used the book Calculus by Adams and Essex, which I found frustrating to work with, because it often left me guessing at what they were trying to do or why they were doing it. I also felt that they exercised a certain lack of rigour. (Which may be due to the subject which would make it hard to derive from axioms.)  Details: Though it would be a complementary text, I'd prefer one which will still hold value as a work of reference at a later point in my studies. I've heard that Rudin's Principles of mathematical analysis is one of the better textst out there, but also read several comments discouraging Rudin's book as a first introduction to real analysis, hence my quest to gather more information and maybe get some more personalised recommendations.  The course: The mandatory course literature will consist of lecture notes, but 4 texts are suggested as recommended reading.   T.M. Apostol, Mathematical analysis. Addison-Wesley (1974) J. Dieudonné, Foundations of Modern Analysis. Academic Press (1960) A. van Rooij, Analyse voor Beginners.Epsilon Uitgaven, no. 6 (2003)   R.S. Strichartz, The way of analysis (1995)   Thanks in advance!
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I was wondering if some one here would please recommend an abstract algebra text book. In particular, I am seeking a text from among one of these:  1) Abstract Algebra by Dummit and Foote  2) Algebra by Michael Artin  3) Topics in Algebra by Herstein.  I was wondering which text is best for a high school student and has great exposition and good problems. My goal is study some algebraic number theory some time later in the near future as I liked elementary number theory.
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I'm interested in quantum mechanics book that uses high level mathematics (not only the usual functional analysis and the theory of generalised functions but the theory of pseudodifferential operators etc, certainly the modern mathematics). If there isn't something similar please give me a reference to the book that is strictly supported by mathematics (given a set of mathematically descripted axioms author develops the theory using mathematics as a main tool).
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I'm a person with graduate level mathematics and some undergraduate statistics background, who'll have to study some basic longitudinal data analysis. I've studied the basics of correlation and regression, measure-theoretic probability, all the necessary distributions (chi², T, F) for the previous, basic tests of confidence intervals etc.  I'm looking for textbooks/lecture notes which are mathematically well-written. By 'well-written', I mean it states the all the necessary results in a mathematically neat way, with or without necessarily going into details of the proof, or by referencing them wherever necessary.   I'm going to use these basic knowledge and results for statistical shape analysis/shape modelling, so may be an inclination to that subject would be preferred, but not absolutely necessary.
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I have read Calculus by Michael Spivak. Now I want to learn additive combinatorics though I have no experience with combinatorics or probability theory. To my understanding, there is a book on the subject by Terence Tao and Vu. Do you think I'll be able to read it thoroughly? Do you have any other suggestions?
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I am looking for a multivariable calculus book that is really physics oriented.  Anyone know of any?  EDIT: My wife is looking to brush up on multivariable at the same time she needs to brush up on the related physics.
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Having studied parametric Bayesian statistics during the two last years, I plan to begin to self-study non parametric Bayesian model during this summer and look for recommendations. I would like the book(s) to cover both the theoritical aspects and the practical ones (with implementation, examples of models ...) Thanks for your recommendations.
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I want to self-study some abstract algebra and cryptography during the summer, so what are some of books that are suitable for self-study? I have very limited background in algebra and none in cryptography, and like to learn by examples. Also, please let me know if there are any books on these subjects with solutions to most of the exercises, so I can check on myself. (I saw 's post about good algebra books, but I would like to focus more on those with good exercises and detailed solutions.)  All suggestions are welcome! Thank you!!
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I searched on this site but I found posts asking for books on complex analysis which I guess is not what I want.   I want a book on problems concerning with roots of unity, argand plane, exponential form, inequalities etc. Some examples : , , .  I don't think these types of problems are covered in a analysis book but I don't know. I think I want a book on algebra of complex numbers.   Are these topics covered in analysis book ? If not, please suggests some books on this topic. I guess my question is bit vague, sorry for that. :).      As suggested in the comments I would like to have books similar to .