Lecture:  MWF 2:00 pm  2:50 pm at PETER 102 
Instructor:  Mareike Dressler 
eMail:  mdressler@ucsd.edu 
Office:  AP&M 6444 
Office Hours: 
M 3:00 pm  4:00 pm at AP&M 6444 W 9:50 am  10:50 am at AP&M 6444 
Discussion: 
C01: M 6:00 pm  6:50 pm at AP&M 7321 C01: M 7:00 pm  7:50 pm at AP&M 7321 
Teaching Assistant:  Nicholas Sieger 
eMail:  nsieger@ucsd.edu 
Office Hours:  W 1:00 pm  3:00 pm, Th 2:00 pm  3:00 pm at AP&M 6414 
Credit Hours:  4 
Prerequisites:  Math 18 or Math 20F or Math 31AH, and Math 20C. Students who have not completed listed prerequisites may enroll with consent of instructor. 
Course description:  This course uses a variety of topics in mathematics to introduce the students to rigorous mathematical proof, emphasizing quantifiers, induction, negation, proof by contradiction, and naive set theory. Students should develop a firm notion of what it means to prove a statement rigorously and be able to write clear proofs using several different strategies by the end of the course. They should learn to move between making full sense of propositions before trying to prove them and considering statements formally so that the symbols can be manipulated even if the overall meaning is unclear. Finally, students should be able to evaluate given proofs, looking at both correctness and elegance. (Required of all departmental majors.) 
Textbook:  Peter J. Eccles, "An Introduction to Mathematical Reasoning", Cambridge University Press, 1997. 
Subject Material:  We will cover parts of Chapters 1  19 of the text. A more complete list of the sections covered can be found in the calendar below. 
Syllabus:  This website acts as our syllabus. 
Exams: There will be three exams in the class:
⭢ You may use one 8.5 x 11 inch sheet of handwritten notes (which may be written on both sides, no photocopies!). No books, calculators, phones, or other aids may be used during exams.
Reading: Reading the sections of the textbook corresponding to the lectures and assigned homework exercises is considered to be part of each homework assignment. You are responsible for material in the assigned reading whether or not it is discussed in the lecture! Homework: Homework will be assigned weekly, and is due on Fridays at 2:00 pm, starting in Week 1.
Homework problems will be uploaded on Canvas and Gradescope.
There will be nine (9) homework assignments in total. They will be graded and will count towards your final grade.
No homework grades will be dropped.
There are two methods to determine your course grade. Your grade will be determined using both methods and then the best grade will be used.
A+  A  A  B+  B  B  C+  C  C 

97  93  90  87  83  80  77  73  70 
Notes
Week  Monday  Tuesday  Wednesday  Thursday  Friday 

0 
Sep 23  Sep 25  Sep 27
Introduction & Chap. 1
Statements, connectives, truth tables


1 
Sep 30
Chap. 2
Implications
Discussion 
Oct 02
Chap. 3
Direct proofs, Arithmetic

Oct 04
Chap. 4
Proofs by contradiction, contrapositive
Homework 1 due


2 
Oct 07
Chap. 5
Induction
Discussion 
Oct 09
Chap. 5
Changing the base case, definitions by induction, Examples

Oct 11
Chap 5; Chap. 6
Strong induction; Set theory, basic definitions
Homework 2 due


3 
Oct 14
Chap. 6; Catchup & Review
Operations on sets
Discussion 
Oct 16
Midterm I 
Oct 18
Chap. 7  8
Quantifiers
Homework 3 due


4 
Oct 21
Chap. 7  8
Cartesian Product and Functions
Discussion 
Oct 23
Chap. 9
Injection, surjection, and bijection

Oct 25
Chap. 9
Inverse
Homework 4 due
Last Day to Drop w/o 'W'


5 
Oct 28
Chap. 10
Counting
Discussion 
Oct 30
Chap. 10
Counting (principles)

Nov 01
Chap. 11
Properties of finite sets
Homework 5 due


6 
Nov 04
Chap. 12
Counting functions and subsets
Discussion 
Nov 06
Chap. 12
Counting functions and subsets

Nov 08
Catchup / Review
Homework 6 due
Last Day to Drop w/o 'F'


7 
Nov 11
Veterans Day (No class) 
Nov 13
Midterm II 
Nov 15
Chap. 14
Counting infinite sets


8 
Nov 18
Chap. 14
Counting infinite sets
Discussion 
Nov 20
Chap. 15
The division algorithm
Homework 7 due

Nov 22
Chap. 15
The division algorithm and applications


9 
Nov 25
Chap. 16
Euclidean Algorithm
Discussion 
Nov 27
Chap. 17
Consequences of the Euclidean algorithm, integral lin. comb., coprime pairs
Homework 8 due

Nov 28
Thanksgiving (No class) 
Nov 29
Thanksgiving (No class) 

10 
Dec 02
Chap. 18
Linear diophantine equations
Discussion 
Dec 04
Chap. 19
Congruence of integers, remainder map

Dec 06
Catchup / Review
Homework 9 due


11  Dec 11
Final Exam
3:00pm6:00pm 