MATH 1365 - Introduction to Mathematical Reasoning

Fall 2013


Course Information (updated Nov. 14, 2013)

Time and place: Section 5: MWTh 1:35 pm - 2:40 pm, 309 Kariotis Hall
Textbook: E. Scheinerman, Mathematics: A Discrete Introduction, Third edition. Cengage, 2012 Make sure you have the correct edition
Instructor: Ryan Kinser
Office and phone: 550 Nightingale Hall, (617) 373-5028.
(From the Nightingale entrance go to the 5th floor, then from the stairway/elevator head straight until you get to Jerzy Weyman's office, then my office is the one to your right.)
Email: r.kinser (at) neu (dot) edu
Office hours: Mon. 3:45-4:45, Tues. 10-11, Wed. 11-12 (These are times when you can drop in and speak with me about anything, without appointment.)
Tutoring center: Hours and sign-up


Course Description

The main objective of the course is to prepare incoming math majors for more challenging mathematical courses at Northeastern by covering the basics of mathematical reasoning and problem solving. The course focuses on learning to write logically sound mathematical arguments and to analyze such arguments. Thus, every assignment and quiz includes a significant writing component. There will be some computations, but the course content can only be mastered through continuous practice of writing mathematical arguments.

We will attempt to cover most of the material in the first five chapters and in Chapter 7 of Scheinerman's book. Here is a more detailed list of topics to be discussed (subject to changes!):

Grading and Expectations

The grading will be based on weekly quizzes (60%), and the final exam (40%). Three lowest quizzes will be dropped.


Homework:
Each reading assignment should be started on the indicated date (or earlier!) and completed before the next class meeting. It is highly encouraged to work with other students on the homework.
Graph Theory, Eulerian paths (go over every edge), Hamiltonian paths (hits every vertex)
Sep 4: read "To the Student" preface (pp. xvii-xviii), Sections 1, 2 and 3; p.2, #1.1; pp.6-7, #3.1-3.3, 3.6, 3.9, 3.12.
Sep 5: read Sections 4 and 5 up to Proposition 5.3; pp.13-14, #4.1-4.5, 4.9; p.22, #5.6, 5.9, 5.11, 5.12.
http://www.numbersimulation.site88.net/ Visualization of composite versus prime numbers, use arrow keys for speed and zoom.

Sep 9: read Section 5 until the end, and Section 6; pp. 22-23, #5.1, 5.2, 5.4, 5.5, 5.22; p.24, #6.1-6.4, 6.9, 6.13.
Sep 11: review Sections 3 - 6; p. 25, #6.10-6.12; Chapter 1 Self Test, pp. 30-32, #3, 8, 9, 11.
Sep 12: Read Section 7. p. 28-29 #7.1, 7.3, 7.4, 7.8, 7.9, 7.10-7.11, 7.12a,c,e, 7.13.

Sep 16: pp. 28-29 #7.15, 7.17-20. Read Section 8. pp. 38-39 #8.3, 8.5, 8.9-8.10
Sep 18: p. 39 #8.12, 8.17-19. Read Section 9. p. 42 #9.2, 9.4-9.5.
Sep 19: p. 43 #9.6, 9.8, 9.10-9.11. Read Section 10. pp. 50 #10.1, 10.3-10.4, 10.10, 10.12

Sep 23: p. 51 #10.11, 10.13. Read Section 11. p. 54 #11.1 (a,b,g,h,i,j), 11.2 (a,b,g,h,i,j), 11.4
Sep 25: Review Sections 9-11. Chapter 2 Self Test p. 70 #2-6, 9, 12.
Sep 26: Read Section 12; p. 64 #12.1, 12.5, 12.9-12.13, 12.16, 12.18, 12.21
Some recreational reading on a very old problem about prime numbers that was recently solved.

Sep 30: Chapter 2 Self Test p. 70 #16, 18, 19; read Section 17 to p. 93 (Note: skip the first paragraph), p. 98 #17.5-17.9.
Oct 2: Read the rest of Section 17. pp 98-99 #17.12, 17.14-17.18, 17.22.
Oct 3: p. 100 #17.23-17.24, 17.26-17.27, 17.32-17.33.

Oct 7: Read Section 22 up to Proposition 22.5 inclusive (you may skip the proof of Theorem 22.2 on p. 137). p. 147 #22.4 a-e, h, 22.5a-c.
Oct 9: Review Sections 11, 12, and 17; Chapter 3 Self-Test p. 117 #10, 11, 13, 14, 17.
Oct 10: Chapter 3 Self Test p. 118 #15, 18. Read Section 22 to the end; Chapter 4 Self Test p. 165 #6-9.

Oct 14: Columbus day holiday
Oct 16: p. 147 #22.16(a-c), p. 134 #21.8
Oct 17: p. 147 #22.16 (d,f), 22.18, Chapter 4 Self Test p.166 #11, 12. Read Section 23 up to Prop. 23.3 inclusive, p. 163 #23.1, 23.2 (b,e,f,g,h).
Optional reading: The Golden Ratio appears in #22.16(f), Some stuff about planar graphs

Oct 21: Read Section 21 Starting with Proof Template 15 on p.128. p. 134 #21.2-21.4, 21.9.
Oct 23: Review the material covered in sections 21-23 (including all the HW). Chapter 4 Self Test p. 165 #13, 14, 16.
Oct 24: Read Section 24. pp. 175-176 #24.2-24.4, 24.14, 24.16, 24.17

Oct 28: p. 176 #24.18, 24.19, 24.20, 24.22. Read Section 26. pp. 186-187 #26.1, 26.9-26.12.
Oct 30: read Section 25, pp. 181-182 #25.2-25.3, 25.5-25.7
Oct 31: p. 182 #25.9-11, 25.15-25.17. Chapter 5 Self Test p. 210 #7-9, 11.
Suggested additional exercises on Pigeonhole Principle.

Nov 4: Review Sections 25 and 26 (including the homework). Chapter 5 Self-Test p. 210-211 #12, 13, 16
Nov 6: Review Sections 24 and 26 (including the homework).
Nov 7: Read Section 35. p. 256 #35.1, 35.2. Read Section 36 up to Proposition 36.4 (inclusive) p. 264 #36.1 (a-d).

Nov 11: Veteran's Day Holiday (observed)
Nov 13: Read the rest of Section 36. p. 265 #36.2, 36.11-36.12, 36.15-36.18.
Nov 14: Chapter 7 Self Test p. 287 #1-6. Review Sections 35 and 36 (including the homework)

Nov 18: Read Section 37 pp 273-274 #37.1, 37.2 (a-c), 37.3, 37.4, 37.10-37.11.
Nov 20: p. 287 Chapter 7 Self-Test #7, 8, 10, 11, 12. Read Section 39 up to Theorem 39.5 (inclusive). p. 283-284. #39.2, 39.3.
Nov 21: Review Sections 35-37 (including all the homework).
Optimally packing circles into a triangle

Nov 25: Read Section 39 till the end. p 284 #39.11-39.14, 39.20, 39.22. p. 288 Chapter 7 Self-Test #12, 15(a), 16, 17.
Visualization of primes and another (you can zoom and drag)
Nov 27-28: Thanksgiving break: Happy Thanksgiving!
Some stuff about perfect numbers and Mersenne primes.

Dec 2: Review all quizzes and homework, complete work assigned in class, evaluations.
Dec 4: Review all quizzes and homework, complete work assigned in class.

Quizzes.
Any material covered up to the date of the quiz is fair game, including material from previous quizzes. I will not give make-up quizzes, so if you will need to reschedule please discuss it with me well in advance of the quiz date.
Quiz 1: Thursday, Sep. 12 Practice, with Solutions.
Quiz 2: Thursday, Sep. 19 Practice, with Solutions.
Quiz 3: Thursday, Sep. 26 Practice, with Solutions.
Quiz 4: Thursday, Oct. 3 (if necessary) Practice, with Solutions.
Quiz 5: Thursday, Oct. 10 Practice, with Solutions.
Quiz 6: Thursday, Oct. 17 Practice, with Solutions.
Quiz 7: Thursday, Oct. 24 Practice, solutions will not be posted.
There will be no quiz on Oct. 31.
Quiz 8: Thursday, Nov. 7 Practice, with longer Solutions and shorter Solutions
Quiz 9: Monday, Nov. 18 Practice, with Solutions.
Quiz 10: Monday, Nov. 25 Practice, with Solutions.

Final Exam: Monday, Dec. 9, 10:30-12:30 in Dodge Hall 119
Joint review session with other sections: Sunday, Dec. 8, 1:00-4:00, location: 105 SH
Allowed during final: one two-sided page of notes, no magnification equipment. Calculators are not allowed.
Last year's final, with Solutions.
Some review problems on functions (solutions won't be written, they can be discussed in class and office hours)
Review problems on Pigeonhole Principle.
Our final exam for Fall 2013, and solutions. The scores are scaled by the formula: scaled score = sqrt(100)*sqrt(raw score).


All students without legitimate conflicts (approved by the instructor) will take the final exam at the scheduled time. Do not make travel plans that conflict with the final exam. Only two finals at the same time or three in one day is a University recognized legitimate reason to be excused from taking the final at the scheduled time. Students with such a conflict should complete a final exam conflict form, available on the registrar’s website. Go to: http://www.registrar.neu.edu/finexsched.html to see the date of your final exam.

If you have a concern about the course or the instructor that cannot be resolved by speaking with the instructor, please contact Professor D.King (Undergraduate Director), 447 LA, x5679, d.king@neu.edu.

It is University policy that no grade, including an incomplete, can be changed after one year. Exceptions must be authorized by the Academic Standing Committee.

All students in the course are responsible for being aware of and following the University's Academic Integrity Policy.