Office | Phone | ||
---|---|---|---|

| (808) 956-4654 | heiner@math.hawaii.edu | |

Spring 2019 | |||

Course title | Course number | Room | Hours |

Introduction to Advanced Mathematics | Math 321 | Kel 414 | MWF 10:30 -- 11:20 |

Reading Course, History of Mathematics | Math 499 | PSB 317 | MWF 9:30 -- 10:20 |

Research Seminar, Fibre Bundles | Math 649 | PSB 317 | TR 9:00 -- 10:15 |

Office hours | and by appointment |

- Syllabus for Math 321
- Look up your grades for Summer 2017: (Use your student ID#)
- HW1, due Friday, January 11th: Out of Velleman. page 6 Problems 1, 4, 6 and page 24 Problems 2, 8.
- HW2, due Monday, January 14th: Out of Velleman. page 24 Problems 12, 14, 16 and page 42 Problem 7.
- HW3, due Wednesday, January 16th: Out of Velleman. page 54 Problem 10. Verify the generalized associative law for an associative binary operation involving expressions involving 4 terms.
- HW4, due Friday, January 18th: Out of Velleman. page 265 Problem 4. Suppose you have n lines in the plane in general position. Into how many regions do the lines separate the plane?
- HW5, due Wednesday, January 23rd: Out of Velleman. page 276f, Problem 6, 10. Solve the Tower of Hanoi problem.
- HW6, due Friday, January 25rd(Monday is fine as well): Show: 7 divides 3^(2n) - 2^n for all natural numbers n. Show: The nth Fibonacci number is even if and only if 3 divides n.
- HW7, due Monday, January 25th: Find integers m and n, so that 165m+135n = gcd(165,135) and k and l so that 228k + 197l = gcd(228,197). Here gcd abbreviates greatest common divisor.
- HW8, due Friday, February 1st: Work out the mod 5 addition and multiplication table.
- HW9, due Monday, February 4th: Out of Velleman. page 223, Problems 4, 14, 20.
- Homework 10, due Wednesday February 6th (a little late is acceptable).
- HW11, due Monday, February 11th: We defined the terms well defined, everywhere defined, injective and surjective for relations. Construct relations that have exactly two of these properties.
- HW12, due Wednesday, February 13th: Show that the composition of two surjective (well defined, everywhere defined) relations is surjective (well defined, everywhere defined).
- HW13, due Wednesday, February 20th: Exercise 1.9 from the notes in relations (below).
- HW14, due Friday, February 22nd: Rewrite solutions of all exam problems (extra credit).
- HW15, due Wednesday, February 25th: Out of Velleman, page 253, Problems 6, 7, 11 (You may submit it late, though there may be more homework for Friday.).
- HW16, due Friday, March 1st: Problems 2.19 from the relations notes. (You may submit it late.).
- HW17, due Monday, March 4th: Problems 2.23 Parts 4, 8, 9, 10 from the relations notes.
- HW18, due Friday, March 8th: Problem 4.13 from the relations notes.
- HW19, due Monday, March 11th: Problem 4.11 from the relations notes.
- HW20, due Wednesday, March 27th: Corrections for Problems 2 and 3 from the exam.
- HW21, due Friday, March 29th: Out of Velleman, page 312ff, Problems 4, 12, 24. Also, if S is a finite set and f a map from S to S, then f is injective if and only if f is surjective.
- HW22, due Friday, April 5th: Construct predecessor sequences for in-class example.
- HW23, due Monday, April 8th: Complete the proof of the Theorem of Schroeder and Bernstein.
- Homework 24, due Wednesday April 10th.
- First exam (Spring 19).
- First exam (Summer 16) with solutions
- Second exam (Summer 16) with solutions
- Relations
- First exam (Summer 15) with solutions
- Second exam (Summer 15) without solutions
- 1st 321 exam Spring 2008
- 1st 321 exam Spring 2010
- 1st 321 exam Fall 2012
- 1st 321 exam Summer 2013
- 1st 321 exam Spring 2014
- 2nd 321 exam Spring 2010
- 2nd 321 exam Fall 2012
- 321 final Spring 2008
- 321 final Spring 2012
- 321 final Fall 2012
- 321 final Summer 2013