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April 8th, 2015, 04:12 PM  #1 
Member Joined: Aug 2012 Posts: 41 Thanks: 0  Studying in advance
Hello, I am planning to go to university in september in pure and applied math. I will take 4 math classes: Linear Algebra Multivariate calc Intro to math thinking (truth table and it is being sold as a preanalysis course) probability The main effort would be on Linear algebra and calc because I expect them to be most challenging. I am following the MIT opencourseware material to prepare for them. I am currently studying in advance, what kind of strategy would you suggest? Should I focus solely on the material I am going to study next semester, and do it exactly as if I was taking classes and being tested on it, or should I take a different approach? Last edited by Spook; April 8th, 2015 at 04:18 PM. 
April 8th, 2015, 06:15 PM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 
I don't recommend this mix of courses. The sort of person who needs multivariate calc and linear algebra is unlikely to benefit from intro to math thinking. But if you take them, my recommendation is to allocate your study time as follows: Linear Algebra: 5% Multivariate Calc: 95% Intro to math thinking: 0% Probability: 0% Alternately, if you have a strong background in matrices from your high school math experience, I recommend Linear Algebra: 0% Multivariate Calc: 100% Intro to math thinking: 0% Probability: 0% Generally speaking, multivariate calc is a hard class and many people will fail. As a math major you shouldn't be one of them, but it will still be hard to get a good grade. Linear Algebra is generally considered an easy class (though important). Intro to math thinking sounds like a typical "math for humanities majors" class and it probably won't help you. Probability will either be easy (if it's a first course in college probability) or trivial (if it's a remedial course). As for your study ahead of time, I would study only calculus. Go through the material as quickly as you can at first, and when it gets hard slow down and take as much time as you need. (This may be immediately.) The other classes will take care of themselves. 
March 21st, 2018, 07:28 AM  #3 
Senior Member Joined: Jun 2015 From: England Posts: 915 Thanks: 271 
If you can get hold of either or both of these books second hand (cheap) they will stand you in great stead for both before, during and after your course. Between them they integrate linear algebra and multivariable calculus very well and will link you to other parts of Mathematics as well An Inroduction to Linear Analysis Kreider, Kuller, Ostberg, and Perkins. AddisonWesley Elementary Multivariable Calculus Kolman and French Wiley 

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