Math 1465 (Intensive Mathematical Reasoning), Fall 2024
| Course Information | |||||
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| Instructor | Class Times | Office Hours | |||
| Evan Dummit edummit at northeastern dot edu |
(Sec 01) MWR 10:30am-11:35am, Ryder 153 (Sec 02) MWR 1:35pm- 2:40pm, 039 Snell Library |
MW noon-1pm MR 3pm-4pm or by appointment Lake 571 or via Zoom |
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| For detailed information about the course, please consult the 1465 Course Syllabus. (Note: any information given in class or on this webpage supersedes the written syllabus.) | |||||
| Problem Session Leader(s) | Recitation Times + Locations | ||||
| Jordan Martino | M, 2:45pm-4:15pm, 114 West Village F | ||||
| Toby Busick-Warner | T, 3:30pm-5:00pm, 311 Ell | ||||
| Ang Barrett | F, 11:45am-1:15pm, 311 Ell | ||||
| We will use Piazza for any course-related discussion: here is the Piazza page. (Note: enrollment in the course is required for access.) | |||||
| All homework assignments will be posted on this webpage (see below). Homework assignments will be collected via Gradescope on Canvas. Please submit scans of your homework pages by 11:59pm Eastern on the due date. Late assignments may be penalized at the grader's discretion. |
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| The instructor will write lecture notes for the course (see below) in lieu of a textbook. If you are seeking additional references, Hammack's "Book of Proof" is an affordable and reasonably good choice. | |||||
| Section 02 (1:35pm-2:40pm) has been moved permanently to 039 Snell Library effective immediately. | |||||
| Midterm 2 has been rescheduled for Monday, Nov 18th. | |||||
| Homework Assignments | |||||||
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| Some Tips on Problem Solving are available as suggestions for the written assignments. | |||||||
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Homework #1, due Tue Sep 10th. (solutions)
Homework #2, due Tue Sep 17th. (solutions) Homework #3, due Tue Sep 24th. (solutions) Homework #4, due Tue Oct 1st. (solutions) Homework #5, due Wed Oct 9th. (solutions) Homework #6, due Tue Oct 22nd. (solutions) Homework #7, due Tue Oct 29th. (solutions) Homework #8, due Tue Nov 5th. (solutions) Homework #9, due Wed Nov 15th. (solutions) Homework #10, due Tue Nov 26th. | |||||||
| Handouts / Lecture Notes | |||
|---|---|---|---|
| Handout | Topics | ||
| Chapter 1: Proofs, Logic, and Sets (28pp, v3.00, posted 9/3) | 1.1 ~ Overview of Mathematical Proof 1.2 ~ Elements of Logic 1.3 ~ Sets and Set Operations 1.4 ~ Quantifiers |
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| Chapter 2: The Integers and Modular Arithmetic (20pp, v3.00, posted 9/20) | 2.1 ~ The Integers, Axiomatically 2.2 ~ Induction 2.3 ~ Divisibility and the Euclidean Algorithm 2.4 ~ Primes and Unique Factorization 2.5 ~ Modular Congruences and The Integers Mod m |
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| Chapter 3: Relations, Orderings, and Functions (31pp, v3.00, posted 10/19) | 3.1 ~ Relations 3.2 ~ Equivalence Relations 3.3 ~ Orderings 3.4 ~ Functions 3.5 ~ Cardinality and Countability |
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| Chapter 4: Elements of Algebra (23pp, v3.00, posted 11/19) | 4.1 ~ Groups 4.2 ~ Fields |
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| Exam Information | |||
|---|---|---|---|
| Exam | Date, Time, Location | Topics | Review Material |
| Midterm 1 (Form A) (sols) (Form B) (sols) |
Wed, October 16th In Class |
Homeworks 1-5 Notes §1.1-2.4 |
Midterm 1 Review Problems (answers) In-class review Thu Oct 10th |
| Midterm 2 (Form D) (sols) (Form E) (sols) |
Mon, November 18th In Class |
Homeworks 6-9 Notes §2.5-3.5.2 (skip 3.3.2) |
Midterm 2 Review Problems (answers) In-class review Thu Nov 14th |
| Final | Fri, December 13th 10:30am-12:30pm Location TBA |
The final is COMPREHENSIVE! Homeworks 1-11 Notes Chapters 1-4.1 |
Review problems to be posted Review dates to be posted |
| Bring your University ID to all exams. You are allowed a calculator and a 1-page 8.5in-by-11in double-sided note sheet, but no other aids beyond writing implements during exams. | |||
| Tips For Success In This Course | |||
|---|---|---|---|
| Attend Lecture | Missing lecture is a very bad idea! If for any reason you cannot make it to a class, you should watch the lecture recording and review notes from someone who did attend. You are responsible for all material covered in lecture. | ||
| Attend Problem Sessions | There are weekly problem sessions run by the course's TAs. The goal of the problem sessions is to provide you a location where you can work with other students on assignments, and also get assistance from a TA. It is highly recommended to attend at least one problem session per week to work on the homework problems. | ||
| Read the Lecture Notes | The lecture notes are the comprehensive source of material for the course. The notes are intended as review material, although many students like to read them as preparation before attending the lecture on the corresponding topics. Please note that the electronic notes are not identical to the material covered in class: this is by design, so as to provide you a slightly different perspective on the material. | ||
| Solve Homework Problems | Much of the learning in this course will take place as you solve the homework problems. Like many other activities, problem-solving and proof-writing are things that are learned by doing them, not by hearing someone else tell you about them or reading about them in a book. As such, the homework assignments are an integral part of the course, and are fundamental to learning the material. It is highly recommended that you look over the homework assignments as soon as they are available, and work on them well in advance of the deadline: many problems will take substantial time and effort to solve, and you should expect to spend as much time as you need to finish the assignments. | ||
| Attend Office Hours | Office hours are specifically reserved for you to receive individual, one-on-one help from the instructor. Office hours will be the most effective when you have already put in effort to learn the material on your own (including trying to solve the homework problems), and when you come in with a list of specific questions or topics you are struggling with. | ||
| Course Schedule | |||
|---|---|---|---|
| The schedule is subject to change! All sections refer to the course lecture notes. | |||
| Week | Schedule | ||
| Week of Sep 2 (class starts 9/4) |
§1.1: Overview of Mathematical Proof §1.2.1: Propositions and Conditional Statements §1.2.2: Boolean Operators and Boolean Logic No homework this week. |
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| Week of Sep 9 | Homework #1 due Tuesday 9/10 on Canvas via Gradescope. §1.3.1: Sets §1.3.2: Subsets §1.3.3: Intersections and Unions |
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| Week of Sep 16 | Homework #2 due Tuesday 9/17 on Canvas via Gradescope. §1.3.4: Complements and Universal Sets §1.3.5: Cartesian Products §1.4.1: Variables and Quantifiers §1.4.2: Properties of Quantifiers |
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| Week of Sep 23 |
Homework #3 due Tuesday 9/24 on Canvas via Gradescope. §1.4.3: Indexed Sets §2.1: The Integers, Axiomatically §2.2.1: Induction §2.2.2: Examples of Induction |
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| Week of Sep 30 | Homework #4 due Tuesday 10/1 on Canvas via Gradescope. §2.3: Divisibility and the Euclidean Algorithm §2.4: Primes and Unique Factorization |
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| Week of Oct 7 | Homework #5 due Tuesday 10/8 on Canvas via Gradescope. §2.5: Modular Congruences and Modular Arithmetic Review for Midterm 1. |
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| Week of Oct 14 (no class 10/14) |
MIDTERM 1 in class Wednesday 10/16 §3.1: Relations §3.2.1: Equivalence Relations No homework this week. |
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| Week of Oct 21 | Homework #6 due Tuesday 10/22 on Canvas via Gradescope. §3.2.2: Equivalence Classes §3.3: Orderings §3.4.1: Functions |
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| Week of Oct 28 | Homework #7 due Tuesday 10/29 on Canvas via Gradescope. §3.4.2: Function Composition §3.4.3: One-to-One and Onto Functions §3.4.4: Bijections |
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| Week of Nov 4 | Homework #8 due Tuesday 11/5 on Canvas via Gradescope. §3.5.1: Cardinality §3.5.2: Countable and Uncountable Sets |
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| Week of Nov 11 (no class 11/11) |
Homework #9 due Wednesday 11/13 on Canvas via Gradescope. §3.5.3: Infinite Cardinalities Review for Midterm 2. |
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| Week of Nov 18 | MIDTERM 2 in class Monday 11/18 §5.1.1: Groups §5.1.2: Dihedral Groups §5.1.3: Symmetric Groups and Cycles No homework this week. |
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| Week of Nov 25 (no class 11/27-11/29) |
Homework #10 due Tuesday 11/26 on Canvas via Gradescope. §5.1.4: Subgroups and Orders |
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| Week of Dec 2 (class ends 12/4) |
Homework #11 due Wednesday 12/6 on Canvas via Gradescope. §5.1.5: Group Isomorphisms §5.1.6: Cosets and Lagrange's Theorem |
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| FINAL EXAM on Friday December 13th, 10:30am-12:30pm | |||