Class Summary - 10/2/16

Instructors:	Mr. Rameel Rizvi
Attendance:	Aidan, Ayyan, Omar, AbdulRafie
Homework:	Read: Chapter 2.5 (this is a review of all main concepts covered in Chapter 2); Problems to solve (found at end of Chapter 2, "Review Problems"):  2.37, 2.39, 2.45, 2.47, 2.48, 2.52, 2.61, 2.63, 2.66
Challenge Problem:	2.76 (please attempt this!)
Class Activity:	Covered chapter 2
Concepts:	Introduced the mathematical function of exponentiation, which takes a "base" b and an "exponent" a and performs b^a (pronounced "b to the ath power"), which is defined as a multiplications of b. For example, 2^3 = 2x2x2 = 8, where 2 is the base and 3 is the power (note: when the power is 2 we call that number a square, and when the power is 3 we call it a cube). Briefly covered the sigma and pi notations for expressing patterns of additions and multiplications (here is a very good link that covers these notations in more detail if you are interested: https://mathmaine.wordpress.com/2010/04/01/sigma-and-pi-notation/). Saw that exponentiation is neither commutative nor associative. Showed why some essential properties of exponentiation hold, such as: (1) x^(y+z) = (x^y)(x^z); (2) (x^y)^z = x^(yz); (3) (a^x)(b^x) = (ab)^x; (4) (a/b)^x = a^x / b^x. Further, we showed that, in general, (a+b)^x does NOT equal a^x + b^x. Also covered powers of 0 (ALWAYS 1!) as well as negative exponents (which just mean to take the reciprocal of the base and then apply the power).
Student Difficulties:	Noticed quite a lot of careless mistakes in the last homework. For your benefit, please try not to rush these problems. You will be less likely to make these types of errors and will also gain more insights into problem solving that will stay with you for the rest of your life. If these errors persist I may start addressing homework problems in class.
Notes	Please hand-in your homework solutions, written in a consistent notebook, in the next class.