reference request - What books should I get to self study beyond Calculus for someone about to start undergrad mathematics?

I am struggling to pick out books when it comes to self studying math beyond Calculus.My situation is as follows. I have taken all math courses at my school (up to Calc BC and AP Stats) and I have scored 5's on all of the exams. I am going to major in math at college next year but I really do enjoy learning in my free time and I am out of material. I have looked at some of the stuff on KhanAcademy, but the videos go really slowly and lack depth, so I would prefer something to read.The only semi math book I have read for fun was Gödel, Escher, B...Read more

reference request - Results in Theoretical CS independent of ZFC

I'm going to ask a quite vague question, since the borderline between theoretical computer science and math is not always easy to distinguish.QUESTION: Are you aware of any interesting result in CS which is either independent of ZFC (i.e. standard set theory),or that was originally proven in ZFC (+ some other axiom) and only later proven in ZFC alorne?I'm asking because I'm close to finish my PhD thesis, and my main result (the determinacy of a class of games which are used to give "game semantics" to a probabilistic modal $\mu$-calculus) is at...Read more

reference request - Are there any statistics texts which give both intuition AND justifications for the equations/methods?

Background: I took multiple statistics classes in both high school and college, but nothing I learned ever stuck. The problem is, things like p-tests, the equations for chi-squared/normal distributions, even the standard deviation are always simply presented as fact, without any proof/justification/motivation for why this equation/method is the correct one.Often, this is because the books are written for people looking to simply apply statistics rather than truly understand it. Usually, not even a calculus-background is assumed, despite the ...Read more

reference request - Simple everyday math

I am looking for a book that contains (instead of crossword puzzles) math problems beginning with simple addition, subtraction, multiplication and division and progresses to more difficult area involving fractions, percents and word problems. I am approaching 70 and world like to keep my mind active, but not having a deep background in math, I need to keep it simple, everyday math situations. Thank you for your assistance with this....Read more

reference request - Rigour vs intuition

Researcher David Tall has written in chapter one of Advanced Mathematical Thinking thatMathematicians often regard the terms “intuition” and “rigour” as being mutually exclusive by suggesting that an “intuitive” explanation is one that necessarily lacks rigour.I can understand how some might think this, but I would like to see some reference(s) that show that mathematicians indeed view that intuition and rigor are opposites.So this is just a reference request. I am not trying to start a discussion here....Read more

reference request - James R. Munkres' TOPOLOGY, 2nd edition: How to check my work?

I'm trying to learn, or revise, some topology from James R. Munkres' TOPOLOGY, 2nd edition. I'm working alone; that is, I'm self-learning. It is quite fun. But the problem is how do I check if I've managed to arrive at a correct solution to an exercise problem? Can I get hold of a solution manual? Or, can I find someone over the Internet with whom I can discuss my solutions? Of course, putting up every other problem at Mathematics Stack Exchange, it seems to me, is not so practical! What would be the best possible for me?...Read more

reference request - Books/subjects for proof practice

So I want to practice writing proofs. I've studied general proof-writing but now I want to learn how to apply that to mathematics. From what I understand, the best and most accessible subjects for that are point-set topology and abstract algebra. I have a book for the latter but what about the former? Which books are good for learning how to write a mathematical proof? I understand that the strategies can differ wildly from area to area but please try to bear with me....Read more

reference request - Book/tutorial recommendations: acquiring math-oriented reading proficiency in German

I'm interested in others' suggestions/recommendations for resources to help me acquire reading proficiency (of current math literature, as well as classic math texts) in German. I realize that German has evolved as a language, so ideally, the resource(s) I'm looking for take that into account, or else perhaps I'll need a number of resources to accomplish such proficiency. I suspect I'll need to include multiple resources (in multiple forms) in my efforts to acquire the level of reading proficiency I'd like to have.I do like "hard copy" materia...Read more

reference request - Journals or Magazines on Study Skills or How to Study Math

I am trying to find only journals or trustworthy magazines which can help math students to study math more efficiently and productively. I am not asking about books in this thread. In particular, I am interested in study skills or tips for math students.I want to do better than Googling for at least 4 days, to find only these three helpful articles that I hope can illustrate what I am pursuing: $1.$ http://ccl.northwestern.edu/papers/2008/PME2008.pdf: Similarly, experts are more likely to refer to multiple definitions within explanations ra...Read more

reference request - Characterization of monotone boolean functions with minimum number of extremal points

Let $B = \{ 0, 1 \}$. For two points $\textbf{x}, \textbf{y} \in B^n$ we will write $\textbf{x} \preceq \textbf{y}$ iff $\textbf{x}_i \leq \textbf{y}_i$ for every $i \in \{ 1, \ldots, n \}$.A boolean function $f: B^n \rightarrow B$ is called monotone if $f(\textbf{x}) \leq f(\textbf{y})$, whenever $\textbf{x} \preceq \textbf{y}$.For a monotone boolean function $f: B^n \rightarrow B$ a point $\textbf{x} \in B^n$ is called a maximal zero of $f$, if $f(\textbf{x}) = 0$ and $f(\textbf{y}) = 1$ for every $\textbf{y}$ such that $\textbf{x} \prec \tex...Read more

reference request - How to relearn undergrad and tackle grad mathematics? Want to become a better mathematician!

I am a student who has just completed their degree in pure math. Unfortunately, my undergrad was a very... Unpleasant time for me due to personal reasons. Although math is accepted as a very "poorly-marketed" and just overall "atrocious" monster of a subject nobody really likes, despite all this, I still appreciate and enjoy it to this day. However, during my undergrad, I really felt like I missed out on a lot (seriously). I am looking to do a lot of self-study and perhaps write notes/record videos on my progress to not only educate myself, but...Read more