Math V2000: Intro to Higher Mathematics
Email: hom [at] math.columbia.eduLocation: 520 Math
Time: TR 11:40-12:55
Office: 613 Math
Office hours: Tuesday 2:30-3:30 pm, Wednesday 10-11 am
TAs: Corrin Clarkson and Hang Xue
Recitation: Tuesday 5-6 pm, 406 Math
Homework
Homework will count for 30% of your final grade, and is due on Thursdays before class in the appropriate box outside of 410 Math. Clearly print your first and last name (as it appears on the registrar) on your assignment. Staple together all of your homework that is due on a given day. Only homework that is turned into the correct location will be graded. You are encouraged to work together with your classmates on the assignments, but the write-up must be in your own words. Late homework will not be accepted. Your lowest homework score will be dropped.Exams
There will be two in-class midterms, scheduled for Tuessday, October 1 and Thursday, October 31. Each midterm will count for 20% of your final grade. The final exam will count for 30% of your final grade, and will be scheduled by the registrar. The date / time for the final is Thursday, December 19, 4:10-7:00 pm in Math 520. No calculators will be permitted for use on the exams. There will be no make-up exams.Help
If you find yourself confused, please seek help sooner rather than later. I will be available to answer questions during my office hours. Additionally, there is the Columbia help room in 406 Math.Schedule & Assignments
Prerequisites: There are no formal prerequisites beyond high-school algebra and some exposure to calculus / limits (Calculus I is more than enough). The biggest requirement is mathematical curiosity and the willingness to think hard about problems that are not necessarily straightforward.Textbook: Transition to Higher Mathematics, by Bob A. Dumas and John E. McCarthy. We will cover most of Chapters 1-8, time permitting.
The schedule below is tentative and subject to change.
Date | Section | Homework from Transition to Higher Mathematics by Bob A. Dumas and John E. McCarthy |
9/3 | Introduction, sets (1.1-1.2) | Exercises 1.1, 1.2, 1.5 Due 9/12 |
9/5 | Sets and functions (1.2-1.4) | Exercises 1.8, 1.10, 1.11, 1.12 (counting the surjections in 1.8 when m>n is extra credit) Due 9/12 |
9/10 | More on functions (1.5-1.7) | Exercises 1.18, 1.21, 1.35 Due 9/19 |
9/12 | Relations (2.1-2.3) | Exercises 2.2, 2.4, 2.7, 2.11 Due 9/19 |
9/17 | More on relations (2.3-2.5) | Exercises 2.5, 2.9 Due 9/26 |
9/19 | Modular Arithmetic, Propositional Logic (2.5, 3.1-3.2) | Exercises 2.16, 2.19, 2.23, 3.1 Due 9/26 |
9/24 | Propositional logic and quantifiers (3.2-3.4) | Exercises 3.4 (ii), (iii), 3.6 (i), 3.7 (i), 3.13 Due 10/3 |
9/26 | Review | Study for midterm |
10/1 | Midterm Exam I | |
10/3 | Proof Strategies (3.5) | click here Midterm I corrections due in class 10/10 Due 10/10 |
10/8 | Induction (4.1-4.3) | Exercises 4.1, 4.13, 4.14 Due 10/17 |
10/10 | More on induction (4.3-4.4) | Exercises 4.12, 4.17, 4.20 Due 10/17 |
10/15 | Divisibility (7.1-7.2) | Exercises 7.2, 7.3, 7.7 Due 10/24 |
10/17 | More divisibility (7.2-7.3) | Exercises 7.4, 7.5, 7.6 Due 10/24 |
10/22 | Fermat's Little Theorem (7.4) | Exercises 7.9, 7.11, 7.14 Due 11/1 at 5 pm |
10/24 | Polynomials (7.5) | Exercises 7.12, 7.16, 7.17 Due 11/1 at 5 pm |
10/29 | Review | |
10/31 | Midterm Exam II | |
11/5 | University Holiday: Election Day | Some non-required reading: Homer's Last Theorem Can you prove that the second equation on Homer's blackboard is false, without using a calculator? |
11/7 | Cardinality (6.1-6.2) | Exercises 6.1, 6.2, 6.3 Due 11/14 Midterm II corrections due in class 11/14 |
11/12 | More cardinality (6.2-6.3) | See below |
11/14 | Finish up cardinality (6.3-6.4) | Exercises 6.6, 6.9, 6.10, 6.11, 6.13, 6.14 Due 11/21 |
11/19 | Limits (5.1) | Exercises 5.2, 5.4 (these are included in the pdf below) Due Monday 12/2 at noon |
11/21 | More limits and continuity (5.2-5.3) | click here Due Monday 12/2 at noon |
11/26 | Natural numbers, integers (8.1-8.3) | click here Due 12/5 |
11/28 | University Holiday: Thanksgiving | |
12/3 | Reals (8.4-8.5) | click here Suggested problems, do NOT turn in |
12/5 | Review | Office Hours:
Tues 12/10 2:30-3:30 pm Wed 12/11 10-11 am Mon 12/16 10-11 am |