I have a problem - I bought a book "Introduction to Time Series and Forecasting" by Brockwell and Davis. The first chapter was ok, but now at chapter 2 I am totally lost - I cannot figure the main idea of the explanation, and I cannot figure the intermediate steps in the author results - so the maths becomes useless. I have no background in stochastic processes.  Can someone recommend a book similar to Brockwell &amp; Davis in contents, but where proofs are given without "It can be shown that..." (with intermediate steps), and which has a more coherent explanations since I do not understand anymore why the author is giving the details of all these propositions in Brockwell book. I need the book for self-study.
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I started by Time Series Analysis by Hamilton, but I am lost hopelessly. This book is really too theoretical for me to learn by myself.   Does anybody have a recommendation for a textbook on time series analysis that's suitable for self-study?
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Edit:  Ok, user  made comment that truly helps narrow the focus of my question. Basically, I'm asking for a self-study course of Mathematical Methods.  Thanks to his recommendation I identified a book that is very close to the answer:  Mathematical Methods in the Physical Sciences by Mary L. Boas  Supposedly, the book covers most of the Math a person needs to learn in order to understand the simulations I presented.  Does this book suit my needs?    Hello,  I have always been interested on the idea to study Math at an Undergraduate level to be able to implement simulations like the followings:  Finite Difference Simulation of the Wave Equation    Heat Equation in Two Dimensions    Besides my precollege experience in Math, I have only been able to do very simple simulations due to my lack of knowledge of Advanced Math. Every time I ask about the inner workings of the simulations I get redirected to papers that look like foreign language to me and, unfortunately, I depend on easy-to-read tutorials to understand them, and while I have found   I'm more interested in reaching the solution myself.  I checked some of the questions related to book recommendations for self-study and while they are very helpful I'm interested in learning by example (There is a book called: "Accelerated C++ Practical Programming by Example" that fits very well my study habits)  Thanks in advance.
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Back in April, I attended a talk at the UMD Math Department Statistics group seminar series called "To Explain or To Predict?". The talk was given by  who teaches at UMD's Smith Business School. Her talk was based on research she did for a paper titled , and a follow up working paper titled .   Dr. Shmueli's argument is that the terms predictive and explanatory in a statistical modeling context have become conflated, and that statistical literature lacks a a thorough discussion of the differences. In the paper, she contrasts both and talks about their practical implications. I encourage you to read the papers.   The questions I'd like to pose to the practitioner community are:   How do you define a predictive exercise vs an explanatory/descriptive one? It would be useful if you could talk about the specific application. Have you ever fallen into the trap of using one when meaning to use the other? I certainly have. How do you know which one to use?
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I am looking for a book (English only) that I can treat as a reference text (more colloquially as a bible) about probability and is as complete - with respect to an undergraduate/graduate education in Mathematics - as possible. What I mean by that is that the book should contain and rigorously address the following topics:   Measure Theory (As a mathematical foundation for probability)   It is of course fine if this theory is addressed with an emphasis on probability and not only for the sake of mathematical measure theory, although the latter would be great too.  Introduction to Probability, i.e. the most common theory a student is exposed to when taking a first course in theoretic Probability. For example: distributions, expected value, modes of convergence, Borel Cantelli Lemmas, LLN, CLT, Gaussian Random Vectors More advanced topics such as: Conditional Expectation (defined through sigma-Algebras), Martingales, Markov Processes, Brownian Motion   I want it to be one book so I can carry a physical copy of it with me and work through the material in my spare time.   Examples:   The book by Jean-Francois Le Gall which can be found here:  but (unfortunately for me) is written in French.  Rick Durrett's book on Probability which can be found here  - the  for this book seems a bit mixed, uncertain about how to weigh that.   I am well aware that it's not easy to meet all of the above criteria simultaneously, but I would be grateful for any recommendation.
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I would like to teach myself measure theory and I am looking for a good introductory textbook at the advanced undergraduate or early graduate level. A reader-friendly text with plenty of examples would be ideal.
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I did a science PhD doing applied bayesian statistics, and I liked it so much that I decided to shift to statistics.  For the last 2-3 years have been working at a firm that has more of a frequentist focus.  It seems to me that the bayesian approach (at least what I learned) has an underlying theory that was laid out and I could understand.  Now I find this - more classical - field fascinating but I am looking for some resources to get a unified view of the matter.  For example, I am learning and applying anovas, F-tests and chi-squares, thinking about degrees of freedom, etc but part of me is looking for deeper understanding that would make it more than just methods.  Does anyone have any suggestions on books or more resources that provide such a unified, deeper focus?
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I am from mathematical background, and I always hated the way they teach elementary probability theory in schools without giving any clue about measure theory.   I want a theoretical book in probability theory, which starts with measure theory and defines everything in mathematical terms. I am also not looking for a measure  theory book. If there is such a book that instead of giving only an intuitive introduction to probability theory, it rather defines everything in details, I would be really grateful to know it.  I would be happy to hear about any reading experience. Being exact in mathematical  language and maybe exercises.  Thanks a lot.
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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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What is a good PDE book suitable for self study?   I'm looking for a book that doesn't require much prerequisite knowledge beyond undergraduate-level analysis.  My goal is to understand basic solutions techniques as well as some basic theory.
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The  that is defined as $Y_{t} = Y_{t-1} + e_t$, where $e_t$ is white noise. Denotes that the current position is the sum of the previous position + an unpredicted term. You can prove that the mean function $\mu_t = 0 $, since $$E(Y_{t}) = E(e_1+ e_2+ ... +e_t) = E(e_1) + E(e_2) +... +E(e_t) = 0 + 0 + \cdots + 0$$ But why is it that the variance increases linearly with time? Does this have something to do with it's not “pure” random, since the new position is very correlated with the previous one? EDIT: Now I have a much better understanding by visualizing a big sample of random walks, and here we can easily observe that the overall variance does increase over time,  and the mean is as expected around zero. Maybe this was trivial after all, since in the very early stages of the time series (compare time = 10 with time = 100) the random walkers have not had yet the time to explore as much.
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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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Does anyone have a recommendation for a book to use for the self study of real analysis? Several years ago when I completed about half a semester of Real Analysis I, the instructor used "Introduction to Analysis" by Gaughan.   While it's a good book, I'm not sure it's suited for self study by itself.  I know it's a rigorous subject, but I'd like to try and find something that "dumbs down" the material a bit, then between the two books I might be able to make some headway.
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What is a good introduction to statistics for a mathematician who is already well-versed in probability?  I have two distinct motivations for asking, which may well lead to different suggestions:   I'd like to better understand the statistics motivation behind many problems considered by probabilists. I'd like to know how to better interpret the results of Monte Carlo simulations which I sometimes do to form mathematical conjectures.   I'm open to the possibility that the best way to go is not to look for something like "Statistics for Probabilists" and just go to a more introductory source.
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I'm taking a course on waves and oscillations using Crawford from the Berkeley series (out of print excluding international copies), and would like to know if anyone has any suggestions for a better book. We cover:    coupled oscillators, forced oscillators,  Fourier analysis,  traveling waves,    and some other topics. Any help with the topic would be appreciated.
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Can anyone help me out with this question I found on my practice paper?  The series $\{y_t\}$ is described by $$ y_t = 5+0.3y_{t-1}+\epsilon_t+0.9\epsilon_{t-1}. $$ Identify the specific ARIMA model. What is the mean of the series $\{y_t\}$?  I think it is a ARMA (1,1) process? is that correct? And how do I calculate the mean of the ARMA model? Is it the same as AR model? If it is then $$ E(y_t) = 5/ (1-0.30) = 7.14?$$    The sample ACF and PACF plot of a series are given above. Appraise the patterns and judge which ARIMA model fit the series. Justify your conclusion.  I identified as the AR(4). Is that correct? Since ACF has an exponential decay and PACF has a cut off? Differencing is not needed as the ACF decreases sufficiently to 0.
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I am interested in self-studying real analysis, and I was wondering which textbook I should pick up. I know all high school mathematics, I have read  (I did most of the exercises).  I have completed a computational calculus course which covered everything up to and including integration by parts (including the substitution method and Riemann sums) I am currently considering:    From what I have heard this is not very well suited for self-study and that while the exercises are extremely difficult, if you take the time they are worth the effort.    I have heard that while Spivak explains proofs in much more detail than Principles, it doesn't cover all of the material in the latter.    I don't know much about this. I have only seen some comments saying that it is an excellent introduction to analysis.    Extra clarification edit: I would prefer a book not to ''dumb down'' the material, something that would not hold my hand through every step, something that would force me to fill in the gaps myself instead of explaining every single step. That is why I am currently leaning towards Rudin, but before I decide I would still like some information on the book by Apostol.
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I am looking for an introductory to intermediate level book on Generalized Linear Models. Ideally, in addition to the theory behind the models, I would want it to include applications and examples in R or another programming language - I hear SAS is also a popular choice. I intend to study it on my own and so it would help if it provided the answers to its own exercises.   You can assume I have taken the traditional year-long courses in calculus and probability theory. I am also familiar with the basics of regression analysis.