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0

My 2cents: Winning Ways by Berlekamp, Conway and Guy is a beautiful but sneaky introduction to advanced mathematics. It's definitely a lot of fun and is great training for a mathematician. Just take it very slow!


1

There can't be more said to make sure you have the fundamentals down very well. Do your best to understand the topics well. Having said that, if you're ready for more, there's plenty of places to go. It depends on your interest and your background. One way to go would be to try to accelerate yourself through the standard Trigonometry, Geometry, ...


3

It usually takes about four years to get through a standard undergrad background in math: single- and multivariable calculus, some basic real and complex analysis, linear algebra, combinatorics and probability theory (as opposed to measure theory), basic group and ring theory, etc. Math is a bit unusual in that people going into it seriously generally do so ...


1

I think that mathematics is just like a language. You can't just fluently speak Spanish if you never have heard a single word in Spanish. You need to gain a lot of knowlegde. First start with the basics: Numbers Basic addition and substraction Multiplication and division It's the same as elementary school, start with the basics. Rome wasn't build in one ...


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There are two reasons for this prejudice Many great mathematicians have produced their greatest works at a young age. For example J.F. Nash received a Nobel prize for actually publishing 3 articles at an age of 25-30. His career after 30 was at best mediocre. Similarly Galois (who unfortunately died at a very joung age) and many others. On the contrary, ...


1

I found this iPhone app that works as an un-typed lambda calculator, it works with successor, addition, addition with successor, multiplication, exponentiation, predecessor and subtraction operations. It shows a step by step process which might be helpful for people who are just starting with lambda calculus. link: ...


0

I am a double major in mathematics and economics. Here's what helps: Undergraduate degree in economics: calculus and an upper-level statistics course. If you really want to impress your professors with research, I highly recommend taking multivariate calculus and differential equations. Linear algebra is not necessary, but it will make life a lot easier. ...


0

You are right. Our time and energy are limited and it is logical to use them in the best manner possible. But reading the "Masters" isn't always the right way to learn mathematics. They may have been masters in their field but that doesn't mean that their books are the best possible books for you. For example, some years ago I tried to read Hardy's classic ...


0

You ask a very fair question, and everyone's suggestions are pretty decent. However, I will explain the biggest jump from high school math and college math, and why you might want to consider not jumping the gun on abstract algebra, analysis, or topology. The biggest difference between high school and college math is that in high school, each lesson is ...


0

The best way to learn hands down is to read the code of an open source 3D framework. See how they implement all of the different operations. Try running one of their basic examples, and put breakpoints in the code to see how it gets executed. To get started, check out Three.js. It's a very popular JavaScript 3D engine, and by reading the code you can get a ...


3

\begin{align} \frac {12x^2-4x}{2\sqrt{4x^3-2x^2+4}}&= \frac{6x^2-2x}{\sqrt{4x^3-2x^2+4}}\\ &= \frac{6x^2-2x}{2\sqrt{x^3-\frac{x^2}{2}+1}}\\ &= \frac{3x^2-x}{\sqrt{x^3-\frac{x^2}{2}+1}}\\ &= \frac{x(3x-1)}{\sqrt{x^3 - \frac{x^2}{2}+1}} \end{align}


0

In fact, they are equal. $f'(x) = \frac {12x^2-4x}{2 \sqrt{4x^3-2x^2+4}}$ both divide 4, we can get $\frac{x(3x-1)}{\sqrt{x^3 - \frac{x^2}{2}+1}}$.


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You can factor a 2 out of the numerator of the derivative, and this will cancel with the 2 in the denominator.



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