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My first suggestion is that you should get used to using mathematics you don't fully understand. I know it seems contradictory, given that you are asking how to learn and not how to use, but there are reasons for doing this. Even mathematicians don't understand perfectly every aspect of the mathematics they are using. Although some may understand the ...


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If you are asking about the UK A level system, A level maths is hard compared to other subjects, probably harder than physics or chemistry and certainly harder than sociology or ethnics studies,etc. Most other subjects you can get credit for some idle waffle but with mathematics that won't get you very far. Don't be put off by a subject because you will ...


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It's all about practice and repetition. That's true about everything from dance and mountain climbing to music and mathematics. The only way to learn is to practice every day, and for several hours every day. If you have trouble finding a solution right away, then take time attacking the problem for a while (several hours to several days). Once you figure ...


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There are different resources for reading on game theory 1) There are online lectures: Game theory 101 which is fairly popular. 2) There is a book: Non Cooperative Game Theory by Tamer Basar, which covers the topic like a subject. 3) There is a nice blog called : www.mindyourdecisions.com Overall to start with you should study the following: 1) Normal ...


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If you would like a book giving challenging problems in linear algebra, modern algebra, and real analysis and complex analysis, which really put your mathematical reasoning skills to a good test and training, as well as forcing you to understand how/when certain classical theorems are used, I highly recommend "Berkeley problems in mathematics". It is a ...


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When I want to study a new subject in math, I find myself a good textbook on the subject, buy a new notebook and sit down at the desk. I work my way front to back through the book, taking very descriptive notes in the notebook. This allows me to have the exact balance of algebra and intuition in my notes. I also don't actually write anything down until I ...


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The Oxford University Maths department seem to have their full set of lecture notes with example sheets on here: https://www0.maths.ox.ac.uk/courses/material/


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If we take a look at say the Schaum's Outline of Logic, it states one rule of conjunction elimination as "From a conjunction, we may infer either of its conjuncts." Thus, given two wffs the output of conjunction elimination is not unique and thus not a function. Also, if we were to reason from Cpq, Crq, Apr to q we would call that a use of disjunction ...


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In terms of the products of the three polynomials, the only possible way of getting an $a^3$ term is from $$(a+b+c)^3=a^3+b^3+c^3+3\sum a^2b+6abc$$ Where the sum is of all the expressions of the same kind. To obtain $a^2b$ from the symmetric polynomials, you need $a\cdot ab$ which comes from $$(a+b+c)\cdot(ab+bc+ca)=\sum a^2b+3abc$$ and substituting the ...


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Let $E$ be the expression equal to $a^3+b^3+c^3$ in terms of symmetric polynomials. Since the reduced expression has no mixed terms, you must have $E = (a+b+c)^3 + E'$, where $$ E' = a^3+b^3+c^3 - (a+b+c)^3 = -3(a^2b +ab^2 +a^2 c +2abc +b^2c +ac^2 +bc^2) $$ To get all of the terms like $a^2b$, we must have $(a+b+c)(a^2+b^2+c^2)$ somewhere in $E'$; after ...


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Have a go at the book Mathematical omnibus. Thirty lectures on classic mathematics by Dmitry Fuchs and Sergei Tabachnikov. This book will engage your mind and point you to very interesting mathematics. Another good book to try out is this one: Vladimir Arnold: Problems for children from 5 to 15.


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To reiterate one of the points that @joel made, mathematics has its own language and oftimes, it is a language barrier that poses a difficult challenge. It sounds as if you are able to translate from "math" to "computer code," and that means, perhaps, that your issue is not so much conceptual as it is the language issue. So, how does one move from being ...


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It sounds like you just need more experience working with the math itself. If you understand pow(2,2) more than $2^2$, then you are doing ok. You just have to get used to the notation and language of math, and that just takes a lot of practice. John Von Neumann was one of the greatest mathematicians of the 20th century, and when asked in an interview how ...



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