<p>I'm starting college this fall and I intent to major in math. Math has always been my passion because I like how numbers and logics can have applications in real life.
How should I spend this summer to be well prepared? I did IB Higher level math and have barely experienced university level math..</p>
<p>Is IB higher level math Calculus? Because I’m fairly sure that if you haven’t done Calc, you’ll have to do it in college. Idk really, but thats my impression.</p>
<p>Yeh it includes calculus and series&differential equation</p>
<p>Calculus and Differential Equations (as a full semester course) are enjoyable and fulfilling because they are manipulative with operations, and things work on a basis in such a way that the major schemes have no trouble clicking after time. You definitely have the first year of university math done with, but that doesn’t necessarily mean that you have 6 more semesters until you get your degree. After you get through Algebra and Calculus, the name of the game becomes proofs and thinking abstractly, and there isn’t a clear cut algorithm for doing that stuff. Calculus definitely involves real thinking too, but the abstract ideas that you see starting with courses in Linear Algebra and Analysis are a step beyond. Typically, at a university you pick a branch of pure math to pursue: either Algebra, Analysis, Discrete Math, or Geometry/Topology. Many students with a real passion however, don’t restrict themselves to just one of these topics. Their practically innate interest makes it enjoyable and thus easy to constantly push the limits of their comprehension, and even more importantly, their very ability to comprehend.</p>
<p>You made the right choice picking series and differential equations because series is the last part of 1st year calculus. You even have a little head-start (emphasis on little) with ordinary differential equations, multivariable calculus, and to a lesser extent, linear algebra.</p>
<p>If universities will let you take final exams to skip courses, I would definitely spend the summer going over multivariable calculus (typically the first course after single variable or high school calculus) which is very brief and easy (overall easier than series). You could even get a big lead in Ordinary Differential Equations when you have extra time. After multivariable calculus though, you could do either differential equations or linear algebra.</p>
<p>For Multivariable Calc, use this book. It’s a bit dry, but it has everything and it’s pretty short:
[Amazon.com:</a> Calculus (With Analytic Geometry)(8th edition) (9780618502981): Ron Larson, Robert P. Hostetler, Bruce H. Edwards: Books](<a href=“http://www.amazon.com/Calculus-Analytic-Geometry-8th-Larson/dp/061850298X/ref=sr_1_2?ie=UTF8&qid=1305928954&sr=8-2]Amazon.com:”>http://www.amazon.com/Calculus-Analytic-Geometry-8th-Larson/dp/061850298X/ref=sr_1_2?ie=UTF8&qid=1305928954&sr=8-2)
Read Parametric equations in chapter 10 and chapters 11-15. Skip section 14.4 on physics, skip any formulas involving 3-d conic sections in section 11.6, and skip regression in section 13.9.</p>
<p>For Linear Algebra (and additionally an excellent text to get used to understanding proofs) use shilov’s text:
[Amazon.com:</a> Linear Algebra (9780486635187): Georgi E.; Silverman, Richard A. (Translator) Shilov: Books](<a href=“http://www.amazon.com/Linear-Algebra-Silverman-Richard-Translator/dp/048663518X/ref=sr_1_1?s=books&ie=UTF8&qid=1305929778&sr=1-1]Amazon.com:”>http://www.amazon.com/Linear-Algebra-Silverman-Richard-Translator/dp/048663518X/ref=sr_1_1?s=books&ie=UTF8&qid=1305929778&sr=1-1)
Neglect chapter 11 in that book.
IMPORTANT: This text is dense and ridiculously difficult to understand. I wouldn’t recommend it at all for learning the material for the first time but only for understanding the proofs after learning linear algebra through MIT’s excellently clear lectures here:
[YouTube</a> - Lec 1 | MIT 18.06 Linear Algebra, Spring 2005](<a href=“Lec 1 | MIT 18.06 Linear Algebra, Spring 2005 - YouTube”>Lec 1 | MIT 18.06 Linear Algebra, Spring 2005 - YouTube)</p>
<p>For ODEs use:
[Amazon.com:</a> Ordinary Differential Equations (9780486649405): Morris Tenenbaum, Harry Pollard: Books](<a href=“http://www.amazon.com/Ordinary-Differential-Equations-Morris-Tenenbaum/dp/0486649407/ref=pd_bxgy_b_text_b]Amazon.com:”>http://www.amazon.com/Ordinary-Differential-Equations-Morris-Tenenbaum/dp/0486649407/ref=pd_bxgy_b_text_b)
Chapters 11 and 12 are honors level topics. You should definitely eventually go over them but they’re comparable theoretical. Chapter 1 is extremely important as a prerequisite to properly understanding Differential equations, but is usually very briefly gone over. The rest is always gone over and tested on.</p>
<p>thanks very much for the detailed reply!! it really gave me the idea of what to do next</p>