Honors Mathematics I

Fall Semester 2019



Instructor: Matt Kerr, matkerr [at] wustl.edu
Office: Cupples I, Room 114
Office Hours: MWF 3-3:50, and by appointment

Assisstant (AI): Chris Felder, cfelder [at] wustl.edu
Office Hours Location: Cupples I, Room 8 (basement)
Office Hours: Monday 4-5, Thursday 2:45-3:45, and by appointment
(The AI runs the discussion sessions.)
Course Outline:

This is the first half of a one-year calculus sequence with an emphasis on rigor and proofs. While self-contained, it will pass only quickly over the more mechanical aspects of calculus. Topics in the first semester include the Riemann-Darboux integral, limits and continuity, differentiation, the fundamental theorem of calculus, sequences and series (of real numbers and of functions), and vector spaces.

Over the course of both semesters of Honors Mathematics (Math 203-204), the goal is to cover the material in Calculus I,II,III (in a more abstract way) and some of Matrix Algebra and/or Differential Equations, depending on the interests of the class and the instructor. This class meets every day of the week, which helps us to achieve these goals.

Prerequisite: A score of 5 on the AP Calculus BC exam, or equivalent.

Class and Exam Schedule:

Lectures are on M/Tu/W/Th from 11-11:50 AM, in Cupples I Rm. 218. Discussion sessions are on Friday at the same time and place. The first class is on Monday Aug. 26 and last class is on Friday Dec. 6. Holidays are Sept. 2 (Labor Day), Oct. 14,15 (Fall Break) and Nov. 27,28,29 (Thanksgiving).

Midterm Exam 1: Thursday, Oct. 10 (in class)
Midterm Exam 2: Thursday, Nov. 14 (in class)
Final Exam: Monday, Dec. 17, 10:30-12:30, in Rm. 218 (Cupples I).

Regarding missed exams, see the Grading Policy section below. Neither notes nor calculators are allowed, but the exams will not be computationally heavy. The Final is cumulative.

Assignments:

These will be collected on Tuesday in class and returned by the end of the week. Solutions will also be posted and may include students' work. Please feel free to come to Instructor and AI office hours to discuss problem sets (and exams) -- that's what they're for!

Grader: David Shen, shen.dawei [at] wustl.edu

HW #1 (due Sept. 4): p. 8 #3; p. 28 #3,5; p. 36 #5,10; p. 45 #11,12,13.
HW #2 (due Sept. 10): p. 57 #9; p. 60 #4,5; p. 64 #5,7(a); p. 70 #5,16; p. 83 #20.
HW #3 (due Sept. 17): p. 94 #12,18; p. 104 #15,31; p. 110 #13; p. 114 #13; p. 116 #5; p. 119 #22; p. 124 #15.
HW #4 (due Sept. 24): p. 138 #21; p. 142 #16; p. 145 #1,5; p. 155 #2,7; p. 168 #24,25,33,39; p. 173 #6,15.
HW #5 (due Oct. 1): p. 179 #5,25,32; p. 186 #1,5,8(a); p. 191 #4; p. 195 #21; p. 209 #21,27; p. 216 #19,26; p. 220 #8
HW #6 (due Oct. 8): p. 237 #27-29; p. 242 #1; p. 249 #30,39-41; p. 257 #4,26,33,42; p. 267 #6,10,32,33
HW #7 (due Oct. 16): p. 278 #7; p. 285 #4,9; p. 291 #22,32; p. 295 #11,13; and show sin(1) irrational
HW #8 (due Oct. 22): p. 303 #26,31; p. 311 #4; p. 319 #2,9,13,18; p. 328 #6,14,23
HW #9 (due Oct. 29): p. 333 #16; p. 339 #1,9; p. 344 #4,11; p. 347 #10,14; p. 356 #31; p. 365 #1,3,6; p. 371 #4,5(b),6,7,13
HW #10 (due Nov. 5): p. 382 #5,17; p. 391 #3,4,14; p. 393 #5; p. 398 #4,7,8,15; p. 402 #3; p. 409 #8,10,16,35; p. 414 #18(a-b); p. 420 #11,17(a)
HW #11 (due Nov. 12): p. 430 #9,18; p. 438 #4,17,24; p. 443 #10,11; p. 456 #3,17,20,21; p. 460 #2,4,12; p. 467 #6,10,13(a-b)
HW #12 (due Nov. 19): p. 477 #4,8; p. 482 #6(b),12,14; p. 487 #3(a),8; p. 492 #9,18; p. 496 #5,7,19; p. 503 #9; p. 508 #7,25; p. 509 #11
HW #13 (due Nov. 26): p. 516 #7,17; p. 524 #6,10; p. 528 #6,12; p. 535 #11,22; p. 539 #1(part 6),10; p. 543 #2(a),5; p. 550 #22

Books:

Tom Apostol, Calculus, Vol. I (2nd Edition), Wiley, 1991

is the text for this class. (Apostol's Vol. II will be the text for Math 204.) You should have your own copy because the homework assignments will come from here, and we will mostly follow it in lectures.

Lectures and Quizzes:

In the calendar below I will post my notes for each lecture (after the class takes place). Click on the "Lec X" link for the notes. The sections covered in the lecture will also be displayed in the table (though these sections may not be covered in full). The "week of" date refers to Monday.

The lecture notes are intended to help you prepare for exams, fill in bits you may have missed in lecture, or even avoid taking notes altogether. They are not intended, however, as a substitute for class attendance and reading the book.

Each Friday discussion section will begin with a short (1-page) quiz. The Friday links will take you to solutions for these quizzes.

Week of ... Mon Tue Wed Thu Fri
Aug. 26 Lec 1
(Intro)
Lec 2
I.1
Lec 3
I.2-3
Lec 4
I.4
Sep. 2 Labor
Day
Lec 5
1.1-7
HW 1
Lec 6
1.8-15
Lec 7
1.16-26
Sep. 9 Lec 8
1.27
Lec 9
2.5-8
HW 2
Lec 10
2.1-4,9-13
Lec 11
2.14-3.2
Sep. 16 Lec 12
3.2-3.6
Lec 13
3.7-3.15
HW 3
Lec 14
3.16-4.3
Lec 15
4.4-4.9
Sep. 23 Lec 16
4.13-4.21
Lec 17
5.1-5.6
HW 4
Lec 18
4.10-12,5.7
Lec 19
5.9
Sep. 30 Lec 20
6.1-6.9
Lec 21
6.10-6.17
HW 5
Lec 22
6.18-6.22
Lec 23
6.23-6.25
Oct. 7 Lec 24
7.1-7.5
Lec 25
7.6-7.11
HW 6
Lec 26
7.12-7.16
Exam 1
Oct. 14 Fall Break Lec 27
8.1-8.7
HW 7
Lec 28
8.7-8.14
Oct. 21 Lec 29
9.1-9.6
Lec 30
9.7-9.10
HW 8
Lec 31
8.15-8.19
Lec 32
8.20-8.27
Oct. 28 Lec 33
10.1-10.6
Lec 34
10.7-10.13
HW 9
Lec 35
10.15-10.17
Lec 36
10.18,10.21
Nov. 4 Lec 37
11.1-11.7
Lec 38
11.8-11.15
HW 10
Lec 39
12.1-12.7
Lec 40
12.8-12.15
Nov. 11 Lec 41
13.1-13.8
Lec 42
13.9-13.14
HW 11
Lec 43
13.18-13.25
Exam 2
Nov. 18 Lec 44
14.1-14.7
Lec 45
14.8-14.13
HW 12
Nov. 25 HW 13 Thanks- giving Break
Dec. 2 HW 14 Final Review


Grading Policy:

Homework and examination grades will be regularly updated on canvas. Your final grade for the semester is determined as follows: HW 40%, midterms 25%, final exam 25%, quizzes 10%. I will drop the lowest two grades you receive on homework and the lowest two grades you receive on quizzes.

Curving and grade scale: In the event that the average score on any exam is less than 75%, all exam scores will be adjusted upward by adding a constant to everyone's score (so that the average is 75%). No adjustment is made if the average is above 75%. The grade scale is as follows:

A+ A A- B+ B B- C+ C C- D F
TBA 90+ [85,90) [80,85) [75,80) [70,75) [65,70) [60,65) [55,60) [50,55) [0,50)

The Pass/Fail policy is that you must get at least a C- to earn a "Pass".

If you have to miss a midterm exam for a legitimate reason, you will be given an excused absence for that exam, and your grade will be calculated from the homework and other taken exams. Of course verified illness and serious family emergency are legitimate reasons. Regarding other conflicts, e-mail me as soon as you know about them.

Verified illness and serious family emergency are in general the only acceptable reasons for missing the final exam. In this event, you will be given a makeup exam. To have any excused absence approved, please contact the Instructor by e-mail (and cc the AI).

This link takes you to the standard university policies on academic integrity.

Academic Support:

While PLTL, Residential Peer Mentoring, etc. do not exist for accelerated courses like Math 203, the Learning Center does help students develop general academic skills (including things like note-taking, time management, and active study skills). If you feel this could be beneficial for you don't hesitate to contact them. But in a class like this your best academic support comes from your peers (discussing in groups to solve harder HW problems is encouraged, though solutions should be written up independently) and from the Instructor and AI in their office hours.