MATH 10003 MATH 19A UCSC

Math 100 Composition of Functions 1. A Composition Exercise Martin H. Weissman Let A = {a, b, c, d}. Let B = {1, 2, 3}. Define functions f : A B, and g : B A, by the following: f (a) = 1. f (b) = 3. f (c) = 3. f (d) = 2. g(1) = a. g(2) = d. g(

Math 100 Evens and Odds, First Proofs Martin H. Weissman To practice proof-writing, in a paragraph style, we will prove some basic facts about arithmetic. 1. Evens and Odds In order to prove things about even and odd numbers, we begin by recalling

Name: Quiz 4 A Inflectional vs. Derivational Morphemes (30 pts) Please divide each of the following words into their component morphemes. For each affix (i.e., not for the root), please state whether it is inflectional or derivational. 1. mysteriou

Math 100 Three Proofs by Induction Martin H. Weissman 1. Division with Remainder Theorem 1. Suppose that x and y are natural numbers, and y = 0. Then there exist natural numbers q and r such that: x = qy + r. 0 r < y. Proof. We prove the theore

Chapter 1 Linear Equations 1.1 Introduction A linear equation (over the real numbers R) in the variables x1 , x2 , , xn is a mathematical equation of the form (1.1) a1 x1 + a2 x2 + + an xn = c, with c and the coefficients a1 , , an some ar

Name: Math 100 Due Friday, November 30, 2:00 pm Homework 8 1. (2 points) Let f : R R be the function given by the formula: f (x) = x3 - x + 1, for all x R. Is f injective? Is f surjective? Justify your answers. Feel free to use the intermediate

Math 100 Function Activity Handout 1. Instructions Martin H. Weissman This is an activity to practice with the definition of functions. The following three pages are meant to be cut into cards, and students are asked to match cards according to wh

Math 100 Homework 5 Martin H. Weissman 1. (3 points) Let S = {a, b, c, d, e, f }. (a) How many subsets of S have 3 elements? For example, {b, d, e} is a subset of S with 3 elements. Note that {b, d, e} = {b, e, d} order does not matter when choos

Math 100 Finite Sets 1. Finite Sets Martin H. Weissman Suppose that A and B are sets, and f : A B is a function. f is called injective if the following sentence is true: If x, y A, and f (x) = f (y), then x = y. f is called surjective if the f