MAT 3013
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# MAT 3013 Foundations of Mathematics

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• ##### Professor:
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taverni

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5.0/5
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Go to Office Hours

Many Small Assignments

Math-heavy

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Nov 13, 2015
| Would highly recommend.

This class was tough.

Course Overview:

First of all, only take this course if you really need to take it. It is very difficult and will require lots of time to complete the homework. However, I am coming out of this course with the best understanding of math that I have ever had. Don't expect to finish the tests. Also, if your are able to keep up on homework, it is likely you will pass.

Course highlights:

Math is pretty general, like 1 + 1 = 2. That makes sense and is neat, but it also gives us an example the sum of two odd numbers is equal to some other even number. Does this work for every odd number combination? Well, lets try, If a, b are integers and a and b are both odd, then a + b is even. Well to prove this, we assume what we know. That a and b are integers and that a and b are odd. Then since a is odd, there exists some k integer such that a = 2k + 1. (Definition of an odd integer, test this on your own and make k any integer (even or odd) and it will always make a an odd integer.) Then since b is odd, there exists some l integer such that b = 2l +1. (Definition of an odd integer) so then a + b = (2k+1) + (2l+1) (substitution) = 2k + 2l +1 + 1 = 2k + 2l + 2 = 2(k + l + 1) Because k and l are integers, and the integers are closed under addition, (k+l+1) = g where g is some integer =2g. (Now to test that this product will be even, make g into any integer you can think of and the product will always be even. This is also equivalent to the definition of even.) so a + b = 2g is even by definition of even. This is a simple proof from the beginning of the semester, the course gets much more complex than this.

Hours per week:

9-11 hours