Midterm Exam 1

Topics

In addition to reviewing the book sections, class notes, and labs, the book has many exercises which you may find helpful in studying. The odd problems have answers in the back of the book.

  1. Sets and Functions
    • Basic operations on sets (e.g., membership, union, difference, intersection, power set, cardinality, cartesian products)
    • Types of functions (including floor and ceiling, see p. 158)
    • Basic proofs using sets or functions
  2. Logic
    • Propositional logic (e.g., logical operators, truth tables, CNF, tautology, valid arguments)
    • Predicate logic (e.g., bound/free variables, quantifiers, interpreting quantifier orders)
  3. Basic Proofs
    • Direct proofs, proof by cases, proof by contraposition, proof by contradiction
  4. Number Theory
    • Core concepts and definitions (e.g., division theorem, divisibility, mod, mod properties, primes, gcd, inverses, congruence)
    • Core algorithms (e.g., Euclid’s Algorithm, modular exponentiation)

The following are some useful problems from the book to try. Note, I’m not saying that the exam is directly related to these problems, just that these are problems that get at some core skills covered on the exam. Please study the notes and try other problems on your own! For the even problems, you may check your answer with me.

  • Section 1.1 Problems 11, 39
  • Section 1.4 Problems 1, 7, 25
  • Section 1.6 Problem 15
  • Section 2.1 Problem 27
  • Section 2.2 Problem 3, 20, 27
  • Section 2.3 Problems 9, 12, 15, 31, 55, 75
  • Section 4.1 Problems 1, 3, 5, 9, 11, 27, 39