Math 184A: Fall 2013
Midterm 2 Solutions and Comments
Instructions: Please write your name on your blue book. Make it clear in your blue book
what problem you are working on. Write legibly and explain
Math 184A: Fall 2013
Midterm 1 Solutions and Comments
Instructions: Please write your name on your blue book. Make it clear in your blue book
what problem you are working on. Write legibly. This exam
Math 184A: Fall 2017
Homework 3
Due 5:00pm on Wednesday 10/18/2017
Problem 1: (Exercise 4.33 in
Bona) Let n be a positive integer. Use a combinatorial
3n
argument to show that n,n,n is divisible by 6
Math 184A, Fall 2017, Prof. Tesler
Homework #5, Due Wednesday November 8, 2017 Answer key
Ch. 6# 1, 2, 5: See answers in book.
6.30.
(a) This can be modelled as a permutation of [10] in cycle form, wi
Math 184A, Fall 2017, Prof. Tesler
Homework #2, Due Wednesday October 18, 2017 Answer key
Ch. 4# 1, 8, 10, 16: See answers in book.
4.3. Counting in two ways: The book sketches a combinatorial proof.
Math 184A, Fall 2017, Prof. Tesler
Homework #9, Due Wednesday December 6, 2017 Answer key
Ch. 12# 3: See answer in book.
11.17. A tree on 0 vertices has chromatic number 0.
A tree on 1 vertex has chro
Math 184A, Fall 2017, Prof. Tesler
Homework #6, Due Wednesday November 15, 2017 Answer key
Ch. 7# 3, 4, 7: See answers in book.
7.28. There are many possible correct answers. We give some examples, an
Math 184A, Fall 2017, Prof. Tesler
Homework #8, Due Wednesday November 29, 2017 Answer key
Ch. 10 #10: See answer in book.
9.41. We prove it by induction on n.
Base case (n = 2): A Hamiltonian cycle i
Math 184A, Fall 2017, Prof. Tesler
Homework #1, Due Wednesday October 11, 2017 Answer key
Ch. 1# 1
and
Ch. 3# 2, 3, 4, 19: See answers in book.
1.19. For the nine players who scored at least one goal
Math 184A, Fall 2017, Prof. Tesler
Homework #1, Due Wednesday October 11, 2017 Answer key
Ch. 1# 1 and Ch. 3# 2, 3, 4, 19: See answers in book.
1.19. For the nine players who scored at least one goal
Math 184A, Fall 2017, Prof. Tesler
Homework #3, Due Wednesday October 25, 2017 Answer key
Ch. 5# 6, 8, 12: See answers in book.
5.12 Here are more details than in the books answer.
(a) Consider a part
November 3, 2017 Math 184A, Prof. Tesler Midterm Answer Key
Name Answer Key Student ID #
Circle the section in which you are enrolled on Tuesdays: 1 /20
Mozhgan Mirzaei Jiaxi Nie 2 /20
BO1 88:50 a.m.
Decision Trees
Ranking and Unranking
Prof. Tesler
Math 184A
Winter 2017
Prof. Tesler
Decision Trees; Ranking and Unranking
Math 184A / Winter 2017
1 / 33
Permutations of [3] in lexicographic order
Lis
Chapter 1. Pigeonhole Principle
Prof. Tesler
Math 184A
Fall 2017
Prof. Tesler
Ch. 1. Pigeonhole Principle
Math 184A / Fall 2017
1 / 16
Pigeonhole principle
https:/commons.wikimedia.org/wiki/File:TooMa
Chapter 10.3
Counting walks in directed graphs
Prof. Tesler
Math 184A
Winter 2017
Prof. Tesler
Ch. 10.3: Counting walks
Math 184A / Winter 2017
1 / 20
Review of dot product
Take two vectors of the sam
Chapter 10.1
Trees
Prof. Tesler
Math 184A
Winter 2017
Prof. Tesler
Ch. 10.1: Trees
Math 184A / Winter 2017
1 / 15
Trees
Stick figure tree
Tree in graph theory
Not a tree
(has cycle)
Not a tree
(not co
Topics in trees and Catalan numbers
See Chapter 8.1.2.1. These slides have more details than the book.
Prof. Tesler
Math 184A
Winter 2017
Prof. Tesler
Catalan numbers
Math 184A / Winter 2017
1 / 22
Ro
Math 184A, Fall 2017, Prof. Tesler
Homework #4, Due Wednesday November 1, 2017 Answer key
On some problems, we show several solution methods and generalizations beyond what was asked.
Most students wi
Math 184A, Fall 2017, Prof. Tesler
Homework #7, Due Wednesday November 22, 2017 Answer key
Ch. 9# 1, 9: See answers in book
9.8.
(a)
(b)
Every permutation of the vertices gives back the same gra
Math 184A, Fall 2017, Prof. Tesler
Homework #9, Due Wednesday December 6, 2017
If you would like to use your homework to study for the exam, please photocopy it
before turning it in.
Chapter 11# 17
Ch
Math 184A, Fall 2017, Prof. Tesler
Homework #4, Due Wednesday November 1, 2017
Note: If you would like to use your homework to study for the exam, please photocopy
it before turning it in.
Chapter 8#
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Homework 4: Due October 30th, 2017
First, do these problems. These will be graded for completion.
2.1: 4, 10, 17, 23, 27, 28b, 32, 33 (The point of 32 and 33 is that this means that any of the standa
Homework 1: Due October 9th, 2017
First, do these problems. These will be graded for completion.
1.1: 8 (just submit I did it if you did it.), 9 (notice theres just one short question at the end.), 1
Homework 5: Due November 6th, 2017
First, do these problems. These will be graded for completion.
2.2: 6, 15
If you are solving Ax = b and your A and b are both known to within 0.01%, and (A) = 1000
Homework 7: Due November 20th, 2017
First, do these problems. These will be graded for completion.
3.2: 8, 28c,d, 39
3.3: 7
Then do these problems. These will be graded for correctness.
1. Write a f
Homework 3: Due October 23rd, 2017
First, do these problems. These will be graded for completion.
1.5: 4, 11, 12
1.7: 10 b,c, 34
Write a function in MATLAB that takes as input a tridiagonal matrix
Math 100A: Abstract Algebra I (UC San Diego, fall 2017)
Homework 5: due November 8 at 5pm
Reminder: no homework due November 15, as there is a midterm that day.
(1) Artin, Chapter 2, exercise 11.3.
(2
Homework 6: Due November 13th, 2017
First, do these problems. These will be graded for completion.
2.6: 6 (you can use MATLAB for all calculations.),
2.7: 12
3.1: 5, 8
3.5: 1, 2, 7, 11, 18a, 23, a
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