MATH 109 - Mathematical Reasoning - Fall 2019

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:

There will be no make-up exams! I.e., you must take your midterms on the scheduled dates at the scheduled times; they will not be offered at an alternate time. It is your responsibility to ensure that you do not have a schedule conflict involving the final exam; you should not enroll in this class if you cannot sit for the final exam at its scheduled time.

⭢ 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.

Homework and late homework policy:

Homework philosophy and collaboration policy:

Canvas:  We will use Canvas for class announcements and additional material uploaded for your convenience and help. You will also be able to check your scores for the graded homework and the tests on it.

Gradescope:  Your midterm exams and final will be scanned and uploaded using an online tool called Gradescope and will be graded within it. As a consequence, exams will not be returned to the students. Instead, a digital version of your exams will be made available after the grading has been completed. An email will be sent from Gradescope when the exams are made available.

Piazza:  We will use Piazza for class discussions. Post on Piazza whenever you're confused about homework, the lecture, the textbook, course logistics, or anything relevant to the course. Do not let yourself be silenced by the fear of looking stupid. Your classmates, the TA, and I will answer. You are strongly encouraged to post messages on Piazza instead of emailing me or the TA directly.

Grading Information

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.

After your weighted average is calculated, letter grades will be assigned based on the following grading scale:

A+ A A- B+ B B- C+ C C-
979390878380777370

The scale may be adjusted to be more lenient (depending on the performance of the class). While the scale may be adjusted to be more lenient, the grade corresponding to a given percentage is guaranteed not to be lower than specified by the above scale.

Notes

Course Calendar

We will cover parts of Eccles' book. The following is a tentative plan and is subject to change or revision. Content covered will be added/updated below as the course progresses (numbers refer to sections in Eccles' book).

Week Monday Tuesday Wednesday Thursday Friday
0
Sep 23
space
space
  Sep 25
space
space
  Sep 27
space
Introduction & Chap. 1
Statements, connectives, truth tables
1
Sep 30
Chap. 2
Implications

Discussion
  Oct 02
space
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
space
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; Catch-up & 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
space
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
space
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
space
Chap. 12
Counting functions and subsets
  Nov 08
space
Catch-up / 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
space
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
space
Chap. 19
Congruence of integers, remainder map
  Dec 06
space
Catch-up / Review
Homework 9 due
11     Dec 11
space
Final Exam
3:00pm-6:00pm
   

Etiquette: Etiquette includes things like giving credit where credit is due, and treating your peers respectfully in class. In addition, here are a few of our expectations for etiquette in and out of class.

Academic Integrity:  Academic integrity is highly valued at UCSD and academic dishonesty is considered a serious offense. Students involved in an academic integrity violation will face an administrative sanction which may include suspension or, in very serious cases, expulsion from the university. Your integrity has great value: Cultivate and protect your academic integrity. Click here for more information on academic integrity and its value.
Academic Accomodations:  Students needing academic accommodations must register with the Office for Students with Disabilities (OSD). The student must provide the appropriate accommodation documentation to the instructor no later than the end of the first week of classes.