Section 2.1   Know the basic terminology in set theory, Cartesian product of sets and know how to find the power set of a set. 

Section 2.2: Operations with sets and the Venn diagrams corresponding to them. Know how to prove that one set is a subset of the other (by showing that both sideis the subset of the other or by switching to logic). Understand the generalized union and intersection of a collection of sets. 

Section 2.3: Know the definitions of one-to-one functions, onto functions, one-to-one correspondence, domain, co-domain, range, images, preimages. Be able to find the inverse of a function and the composition of two functions, image and preimage of a set for a given function. Know the floor and ceiling functions.  Be able to come up with examples for functions that have or does not have certain properties for integer domain and range and know how to justify that these properties hold or not..

Section 2.4:   Be familiar with sequences, the Sigma notation and be able to use it and generate it.  Understand what it means that a set is countable or uncountable and how to justify if it is or not.

Section 3.1: Be familiar with the linear and binary search algorithms and with algorithms for locating minimum and maximum elements in a list. Have a working knowledge if the pseudo code used in our text. 

Section 3.2: Know what it means that f(x) is O(g(x)) and know how to apply it in particular situations by finding a constant C and k from the definition. Know how to use the standard results (polynomials, sums and products of funcions) to compute the best possible big-O estimate for a given function. 

Section 3.3: Understand how to compute the complexity of an algorithm and how to express the complexity using big-O notation. 

Section 3.4: Know the following terms and notations: prime, composite number, integer a divides b, . Understand the statement of the division algorithm. Be able to determine if a number is a prime (remember the sqrt(n) theorem). Know the definition and examples dealing with modular arithmetic. Be able to do simple proofs that are the same or similar to class, book and homework  examples.  Be able to code or decode a simple message using Ceaser's cipher.

Section 3.5: Understand the process of prime factorization, be able to find gcd and lcm using prime factorization.

Section 3.6: Know how to use the Euclidean algorithm to find gcd of two integers. Be able to convert numbers from decimal to binary form and vice versa, also for hexadecimal form.

Section 4.1 again:  review the basic ideas of mathematical induction. Review your mistakes (if any) from test 1.

Section 4.2  Understand the need for the strong induction and its basic idea. Understand the use of second principle of  mathematical induction for cases presented in the book. Remember that often more than one step is needed in the basis step.

Section 4.3: Understand how functions, sequences and sets can be defined recursively. Be able to .....  Know the Fibonacci sequence and be able to use mathematical induction to prove statements about the Fibonacci numbers. 

Section 4.4: Be familiar with all recursive algorithms in our text, understand the difference between recursive and iterative algorithms and be able to write pseudo codes for simple recursive algorithms.

Recommended  problems to review: