MATH 1365 - Introduction to Mathematical Reasoning

Fall 2012


Course Information (updated Oct. 19, 2012)

Time and place: Section 1: MWTh 10:30 am - 11:35 am, 158 Ryder Hall
Section 2: MWTh 1:35 pm - 2:40 pm, 283 Ryder Hall (#24 on the campus map)
Textbook: E. Scheinerman, Mathematics: A Discrete Introduction, Third edition. Cengage, 2012 This is a new edition from previous years
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 2:45-3:45, Tues noon-1, Wed 12:30-1:30
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. 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!):

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

Attendance will be taken and you are expected to be present for every class. It is your responsibility to be aware of any changes in the syllabus announced in class. Students are responsible for all information given when they are absent.


Homework:
Each reading assignment should be started on the indicated date (or earlier!) and completed before the next class meeting.
Sep 5: 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 6: 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 10: 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 12: review Sections 3 - 6; p. 25, #6.10-6.12; Chapter 1 Self Test, pp. 30-32, #3, 8, 9, 11.
Sep 13: 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 17: pp. 28-29 #7.15, 7.17-20. Read Section 8. pp. 38-39 #8.3, 8.5, 8.9-8.10
Sep 19: p. 39 #8.12, 8.17-19. Read Section 9. p. 42 #9.2, 9.4-9.5.
Sep 20: 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 24: 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 26: Review Sections 9-11. Chapter 2 Self Test p. 70 #2-6, 9, 12.
Sep 27: Read Section 12; p. 64 #12.1, 12.5, 12.9-12.13, 12.16, 12.18, 12.21

Oct 1: 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 3: Read the rest of Section 17.  pp 98-99  #17.12, 17.14-17.18, 17.22.
Oct 4: p. 100 #17.23-17.24, 17.26-17.27, 17.32-17.33.  

Oct 8: Columbus day holiday
Oct 10: Review Sections 11, 12, and 17; Chapter 3 Self-Test p. 117 #10, 11, 13, 14, 17.
Oct 11: 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 15: Chapter 3 Self Test p. 118 #15, 18. Read Section 22 to the end; Chapter 4 Self Test p. 165 #6-9.
Oct 17: p. 147 #22.16(a-c), p. 134 #21.8
Oct 18: 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 22: Read Section 21 Starting with Proof Template 15 on p.128. p. 134 #21.2-21.4, 21.9.
Oct 24: Review the material covered in sections 21-23 (including all the HW). Chapter 4 Self Test p. 165 #13, 14, 16.
Oct 25: Read Section 24. pp. 175-176 #24.2-24.4, 24.14, 24.16, 24.17

Oct 29: p. 176 #24.18, 24.19, 24.20, 24.22. Read Section 26. pp. 186-187 #26.1, 26.9-26.12.
Oct 31: read Section 25, pp. 181-182 #25.2-25.3, 25.5-25.7
Nov 1: 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 5: Review Sections 25 and 26 (including the homework). Chapter 5 Self-Test p. 210-211 #12, 13, 16
Nov 7: Review Sections 24 and 26 (including the homework).
Nov 8: 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 12: Veteran's Day Holiday (observed)
Nov 14: Read the rest of Section 36. p. 265 #36.2, 36.11-36.12, 36.15-36.18.
Nov 15: Chapter 7 Self Test p. 287 #1-6. Review Sections 35 and 36 (including the homework)

Nov 19: Read Section 37 pp 273-274 #37.1, 37.2 (a-c), 37.3, 37.4, 37.10-37.11.
Nov 21-22: Thanksgiving break: Happy Thanksgiving!

Nov 26: 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.
Optimally packing circles into a triangle
Nov 28: Review Sections 35-36 (including all the homework).
Nov 29: 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)

Dec 3: Review all quizzes and homework, complete work assigned in class, evaluations.
Dec 5: Review all quizzes and homework, complete work assigned in class.

Quizzes: (usually every Thursday)
Quiz 1: Thursday, Sep. 13 (on Sections 3-6). Practice, with Solutions.
Quiz 2: Thursday, Sep. 20 (on Sections 7-8). Practice, with Solutions.
Quiz 3: Thursday, Sep. 27 (on Sections 9-11). Practice, with Solutions.
Quiz 4: Thursday, Oct. 4 (on Sections 3-12). (Practice by reviewing previous quizzes and HW)
Quiz 5: Thursday, Oct. 11 (on Sections 11, 12, 17). Practice, with Solutions.
Quiz 6: Thursday, Oct. 18 (on Sections 17, 22). Practice, with Solutions.
Quiz 7: Thursday, Oct. 25 (on Sections 21-23). Practice, with Solutions.
There will be no quiz on November 1.
Quiz 8: Thursday, Nov. 8 (on Sections 24, 26). Practice, with Solutions.
Quiz 9: Monday, Nov. 19 (on Sections 24-26, 35, computational part of 36). Practice, with Solutions.
Quiz 10: Thursday, Nov. 29 (on Sections 35-37). Practice, with Solutions.

I will be available for questions during finals period by appointment.
Joint review session with other sections: Wednesday, Dec. 12, 1:00-3:00, location: 315 SH

Final Exam: Friday, Dec. 14, 10:30-12:30 in Behrakis Health Sciences Cntr 220
(Allowed: one two-sided page of notes, no magnification equipment. Calculators are allowed now.)
There will be 11 problems, your best 10 will be counted. Last year's final, with Solutions.
Most of the quizzes from both sections, most with solutions (one big archive)
Some review problems on functions.
Reserve approx. 5 minutes before the final and ONLY click this link just before you go. (You might have to wait a few seconds for it to start...)
Solutions to our Fall 2012 final


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. 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.