### Math 1C03: Introduction to Mathematical Reasoning, Winter 2018

#### Basic Course Information:

• Lectures: Mondays 9:30-10:20AM, Tuesdays 10:30-11:20AM, Thursdays 9:30-10:20AM, Hamilton Hall 302.
• Instructor: Prof. Megumi Harada
• Office: Hamilton Hall 325
• Office hours: Mondays 10:30--11:30AM, Tuesdays 11:30AM--12:30PM, Wednesdays 11:30AM--12:30PM, or by appointment. Subject to change.
• Tutorials: Wednesdays 3:30--4:20PM and 4:30--5:20PM. The first meeting of tutorials is Wednesday January 10th. Your TA is Fletcher Gates.

#### Course Syllabus and Overview:

The required text for this course is An Introduction to Mathematical Thinking: Algebra and Number Systems by William J. Gilbert and Scott A. Vanstone (ISBN: 0131848682). The course syllabus,, gives a more detailed discussion of what to expect in this course. You may also wish to consult my Undergraduate FAQ.

#### Announcements:

Look here for general Updates, Announcements, and general course handouts also, such as notices of last-minute changes to office hours. (Warning: Some announcements specific to an inclass-test or a particular homework problem may be posted in the subject-specific sections below.)

• The first meeting of Tutorials will be Weds Jan. 10.
• The TA (Fletcher Gates) has office hours on Tuesdays at the Math Help Centre, 6:30--8:30PM.
• The review session for Test 1 will be Friday, January 19, 2:30PM--4:30PM, HH/109.
• The material to be covered for Test 1 will be all of Chapter 1 of the textbook. The exception is ``proof by contradiction'', which will not be on Test 1.
• Here is a Practice Test 1.
• Here are Sample Solutions to Practice Test 1.
• Here is a list of suggested review problems for Test 1.
• Test 1 locations and class breakdown:
• Last names ADE -- KAY: Go to BSB/137.
• Last names KAZ -- ZY: Go to (usual classroom) HH/302.
• Here are Sample Solutions to Test 1. These are samples only; there are other solutions that could earn full marks.
• The review session for Test 2 will be Wed. Feb. 7th, BSB/119, 5:30--7:20PM.
• Office hours are CANCELLED for Weds. January 31. I will re-schedule an extra office hour next week in preparation for Test 2.
• The material to be covered on Test 2 will be Chapter 2, Sections 1-3. In addition, I reserve the right to put on a question that requires a proof by contradiction.
• Here is a Practice Test 2.
• Here are Sample Solutions to Practice Test 2.
• You will be allowed to use a McMaster standard calculator for Test 2.
• Here is a list of suggested review problems for Test 2. In addition, I suggest the problems from the optional homework for Week 4, posted above.
• Due to the cancelled office hour on Weds Jan. 31, I will have an extra office hour Monday Feb. 5th, 11:30AM--12:30PM.
• Test 2 locations and class breakdown:
• Last names AA -- LIN: Go to MDCL / 1110.
• Last names LIO -- ZY: Go to (usual classroom) HH/302.
• For Monday February 12th, office hours will be 11:30AM--12:30PM instead of the usual 10:30AM--11:30AM.
• Here are Sample Solutions to Test 2. These are samples only; there are other solutions that could earn full marks.
• Test 3 will be Tuesday, March 6, during class time. Rooms TBA.
• The review session for Test 3 will be Friday March 2, HH/109, 2:30--4:20PM.
• Here is a Practice Test 3.
• Here is a list of suggested review problems for Test 3.
• NOTE: Fletcher's office hours are cancelled for the day of the Test 3, Tuesday March 6.
• Here are Sample Solutions to Practice Test 3.
• Test 3 location: Everyone should go to the testing room T13/123.
• Material to be covered on Test 3: everything in Chapter 3, up to and including the ``Linear Congruence Theorem''.
• Here are Sample Solutions to Test 3. These are samples only; there are other solutions that could earn full marks. (Update: typo alert on my solution to 4(c). In the last bit of the argument it should be that b is equal to a times a to the power p-2 (not p-1). Thanks to Fletcher for noticing.)
• Office hours for Monday March 19 are cancelled; a make-up office hour is scheduled for Tuesday March 20, 9:30--10:30AM.
• Test 4 will take place Monday March 26, during class time. Rooms TBA.
• Material to be covered on Test 4: Chapter 3 Section 6 (Chinese Remainder Theorem and Generalized Chinese Remainder), Chapter 4 Sections 4.1 and 4.2 (induction and strong induction, recursion), and Chapter 6 Section 1 (Functions).
• The review session for Test 4 will take place Fri. Mar. 23, HH/109, 2:30-4:20pm.
• Here is a Practice Test 4.
• Test 4 locations and class breakdown: (same as Test 1)
• Last names ADE -- KAY: Go to BSB/137.
• Last names KAZ -- ZY: Go to (usual classroom) HH/302.
• Here are Sample Solutions to Practice Test 4.
• Here is a list of suggested review problems , assembled kindly by Fletcher, for Test 4.
• Here are Sample Solutions to Test 4.
• Fletcher's office hours for Tuesday March 27 are cancelled. Sorry for late notice!
• Fletcher's last set of office ours (Tuesday April 3) are cancelled. Again, sorry for late notice.
• The review session for the final exam will take place Thursday April 19, TSH B128, 3:30--5:30pm.
• I will hold extra office hours (HH/325) during the final exam period as follows:
• Friday April 13, 9:30--11:00am,
• Monday April 16, 9:30--11:00am and 12:30--1:30pm,
• Thursday April 19, 9:30--10:30am.
• The final exam will be cumulative, covering the entire course, but with some emphasis on the last few weeks of class. There will be 12 questions in total, out of which you are expected to choose 10. There is no `essay question' -- however, I ask you up-front to understand that for ANY problem, you are welcome to simply `write an essay' on what you know about the topics that are relevant for that problem (e.g. give a definition, describe an algorithm, etc.) in order to earn partial marks.
• The chapters / sections in the book for which you are responsible are as follows: all of Chapter 1, Chapter 2 Sections 2.1, 2.2 and 2.3, Chapter 3 Sections 3.1, 3.3, 3.4, 3.5, 3.6 and 3.7, Chapter 4 Sections 4.1 and 4.2, Chapter 6 Sections 6.1--6.6, Chapter 7 Section 7.4.
• Calculators will NOT be permitted at the final exam. I have endeavored to make sure that you can solve all problems without resorting to a calculator.
• Here is a Practice Final Exam. The actual final exam will look almost identical to this one. In particular, please note the instructions on the first page: you MUST cross out, with a clear `X', the boxes for the problems that you do not wish to have marked.
• Here are Sample Solutions to the practice final exam.
• Here is a list of suggested review problems , assembled kindly by Fletcher, for the final exam.
• Here are notes from Fletcher's review session .

#### Course resources:

There are many resources available to you to aid you in your studies in this course. Some are listed below. Feel free to make suggestions for things to add to this list.

#### Tests and Exams:

Look here for announcements as the semester goes on.