Which books/topics should I read to understand the mathematics behind Quantum physics and Astrophysics?
Mathematical topics and branches needed to study and understand quantum physics include the following :Linear algebra , Ordinary differential equations and Partial differential equations (useful to understand or solve the Schrodinger equation for example), Calculus , Probability and statistics , Fourier transforms , Complex numbers , Hilbert spaces , linear operators and spectral theory , eigenvectors and eigenvalues , matrix operations , special functions (Legendre polynomials , Bessel functions , etc) , mathematics related to classical , Lagrangian , and Hamiltonian mechanics , and group theory (mostly for advanced quantum physics ).Here is a helpful introductory book about quantum physics :Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles, by Robert Eisberg, Robert Resnick.Some useful books dealing with mathematics for (quantum and general) physics :Mathematical Tools for Physics, by James Nearing.Mathematics of Classical and Quantum Physics, by Frederick W. Byron, Robert W. Fuller.Mathematical Methods in the Physical Sciences: Mary L. Boas.See also the following link :Mathematical formulation of quantum mechanicsIn the Schaum book series one can find many educational books about various mathematical topics .For astrophysics , algebra and (multivariate) calculus are generally required , then other math topics are required depending on one’s area of specialty in astrophysics .For example , relativistic astrophysics and cosmology require the study of tensor analysis , and a number of topics in physics are usually chosen for study , such as thermal physics , electromagnetism , and quantum mechanics . Thus at least a good part of the mathematics for quantum physics would be needed for studying the physics related to astrophysics .See for example the following link :Department of Astrophysical Sciences
What levels and areas of math are involved in Bill Chen's book, the Mathematics of Poker? How much math should one know before attempting to read the book?
The book mainly doesn't use anything beyond calculus. There are a couple difference equations that are solved, and some standard beginning and maybe intermediate probability and statistics things. We tried to separate the more technical stuff from the basic algebra, so that readers could skip more complex derivations if they wanted.
Simple Mathematics Proof & mathematics book?
Q1. Show that any integer square leaves remainder 0 or 1 on division by 4. Q2. Hi, I'm high school senior going to graduate in feb 2008. I want to study Mathematics in college as my major. As a high school student, I've learned Calculus, Statistics, but I had no chance to study advanced or 'REAL' mathematics such as the proof system of mathematics. But I want to really change myself. In these days, I am reading 'Mathematics and its history' and 'The history of pie' to advance my mathematics. I love mathematics and desire to be good mathematician. Can you recommend me two kinds of books? The first is basic books such as introduction to~(I am stumbling with above two mentioned books sometimes). The second is problem solving book including advanced (AMC level questions) level problems. Thank you very much, merry christmas!!
What books in math, physics and chemistry should I read?
Mathematical Methods in the Physical Sciences is probably a perfect book for you because it will teach you the math you will need for all of your chemistry and physics (and probably all of the math you will be doing). Unfortunately, it is not as problem oriented as you prefer but still has plenty of problems to work. For chemistry: why not just work through a book like Head First or Barron's for chemistry? I'm going to assume that you will be starting out with general chemistry at school. Probably your best bet is to find some way to read about each of the topics in gen chem until you feel like you understand them, and then work practice problems until you feel really comfortable with them. I can't think of a single book in particular that will be best for this. Instead, check out a couple books at your local library and decide which one has explanations which make the most sense to you.
Which math book did Feynman read?
Hello feynman did say in an interview I watched on youtube that he had different "tools" to approach a problem when he was a graduate student.. and he sais that he had those tools because (if I recall correctly) he was kinda weak or fresh in some math class and his teacher gave him a book (about algebra I think but I could be wrong) Does anybody know the name of that book? I knew it and downloaded it.. but I cant find it neither I remember it nor I can (untill now) find the video were he was talking about that story... does anybody know? The only thing I can remember is that the video was about his ttransferfrom MIT to oxford (I think) and he was talking about the differences and things that happened in the fraternity and stuff like that..
How does one go about reading a math book?
Paul Halmos, who was famous as a mathematical expositor, had some great advice about this:Don't just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?That is, try to deconstruct and reconstruct each result. What is the motivation behind it? What is an example where it applies? What is an example where it does not apply? What were the key strategies used in the proof? Why is each assumption needed, and can you find explicit counterexamples if you delete an assumption? How does the theorem connect with other results?Reading as actively as possible, by thinking about these kinds of questions and doing a bunch of exercises, is very important. Textbooks often create the impression that problem-solving is a separate activity done after reading the material (if at all), since they often relegate the exercises to the end of each chapter. Instead, I recommend interweaving reading with problem-solving (the problems can both be those provided in the book and questions that you come up with while trying to deconstruct and reconstruct the results).Also, math is a connected web of ideas but books are inherently linear, so it is especially helpful (with a well-written book) to reread chapters to reinforce your understanding and look for connections between ideas.Clearly this is a very time-consuming process, requiring dedicated effort. But studying in this way should help give a much deeper understanding of the material compared with passive reading.
What can I do when I get stuck reading a math book?
If you get stuck reading a math book, what is important is how you react to being stuck and what strategies you have for overcoming these problems.First. Take a rest for a minute.Second. Skim read the learning material, the activities and the assignment questions to get an overview of what you need to do.Then read everything again, with concentration; mark important sections and parts that aren’t clear. While you’re reading, think about the material and ask yourself questions about it; then answer the questions in your own words. If you struggle to answer the questions, it could be you don’t fully understand what you're reading. Don't forget to Make notes – this helps focus your mind. Also note the sections you don’t fully understand so that you remember to go back to them.