Marquette University

Department of Mathematics, Statistics and Computer Science

Wim Ruitenburg's Spring 2018 MATH/SCS 4320 5320 -101. Number Theory

Last updated: February 2018
Comments and suggestions: Email   wim.ruitenburg@marquette.edu

All problems apply to both 4320 and 5320 classes unless stated otherwise.

Due date if any Fuchsia means graded homework.

12-14 February
  • Section 2.5: 8a.
  • Section 2.5: 2, 5a, 6.

5-9 February
  • Section 2.5: 1.
  • Section 2.4: 5a, 8.
  • Section 2.4: 2cd, 4ab, 6.
  • Section 2.3: 19a, 20abc, 21.

29-2 Jan/February
  • Section 2.3: 4b, 12, 14, 18.
  • Section 2.3: 2, 6.
  • Section 2.2: 2, 4.
  • Section 2.1: 1, 2, 10.

22-26 January
  • Convert the decimal number 99 into binary.
    Convert the binary number 10101 into decimal.
  • When we expand (a+b)^13, what is the (binomial) coefficient in front of a^9*b^4? Write your final answer as a decimal number.
  • Section 1.2: 1, 8.
  • Think of a good more general formula than the one in Section 1.2.2. Then try to prove this more general formula to be correct.
  • Consider the sequence a_1, a_2, a_3, a_4, a_5, ... defined by
    • a_n = 1/(1*2) + 1/(2*3) + 1/(3*4) + 1/(4*5) + ... + 1/(n*(n+1)).
    • By trial and experiment find a `closed' simple expression for a_n.
    • Prove by induction on n that this `closed' simple expression for a_n is always correct.
  • Section 1.2: 2, 3.

17-19 January
  • Section 1.1: 8.
    Also, compute 12! (twelve factorial).
    Also, consider the sequence a_1, a_2, a_3, a_4, a_5, ... defined by
    • a_1 = 1, and for all n >= 2 we have a_n = a_1 + a_2 + a_3 + ... + a_(n-1).
    • By trial and experiment find a `closed' simple expression for a_n.
    • Prove by induction on n that this `closed' simple expression for a_n is always correct.
  • Section 1.1: 1ae, 2, 9.