Math 1365 (Introduction to Mathematical Reasoning), Fall 2023
| Course Information | |||||
|---|---|---|---|---|---|
| Instructor | Class Times | Office Hours | |||
| Evan Dummit edummit at northeastern dot edu |
(Sec 02) MWR 1:35pm-2:40pm, 430 Dodge (Sec 14) MWR 4:35pm-5:40pm, 305 Shillman |
MWR 3:00pm-4:00pm or by appointment Online, via Zoom |
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| This section of Math 1365 is a more intensive pilot program for a new course being developed. For detailed information about the course, please consult the 1365 Course Syllabus. (Note: any information given in class or on this webpage supersedes the written syllabus.) | |||||
| Problem Session Leader(s) | Recitation Times + Locations | ||||
| Devin Brown |
M, 11:45am-1pm, 220 Ryder | ||||
| Ryan Kannanaikal and Molly Sager | T, 11:45am-2:45pm, 016 International Village | ||||
| Sam Lowe |
F, noon-2:00pm, 209 Ryder | ||||
| We will use Piazza for any course-related discussion: here is the Piazza page. | |||||
| 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. | |||||
| As of Wed Nov 8th, classes have returned to being fully in person. | |||||
| The final exam review sessions are from 11:45am-1:45pm in 202 Shillman on Thu Dec 7, Sat Dec 9, Mon Dec 11 . The final exam itself is from 3:30pm-5:30pm in 103 Churchill on Wed Dec 13 . | |||||
| 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 12th. (solutions)
Homework #2, due Tue Sep 19th. (solutions) Homework #3, due Tue Sep 26th. (solutions) Homework #4, due Tue Oct 3rd. (solutions) (note: problem 3 was moved to homework #5) Homework #5, due Tue Oct 10th. (solutions) Homework #6, due Tue Oct 24th. (solutions) Homework #7, due Tue Oct 31st. (solutions) Homework #8, due Tue Nov 7th. (solutions) Homework #9, due Tue Nov 14th. (solutions) Homework #10, due Thu Nov 30th. (solutions) Homework #11, due Thu Dec 7th. (solutions) | |||||||
| Handouts / Lecture Notes | |||
|---|---|---|---|
| Handout | Topics | ||
| Chapter 1: Proofs, Logic, and Sets (28pp, v2.50, posted 9/5) | 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, v2.50, 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, v2.55, posted 10/21) Updates in v2.55: Added properties of cardinality 8 and 9 (pg 25) |
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 (21pp, v2.00, posted 11/19) | 4.1 ~ Groups 4.2 ~ Fields |
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| Lecture Slides | |||
|---|---|---|---|
| These are the slides for the Zoom lectures. | |||
| Date | Material | ||
| Wed, Oct 4th | Lecture 12: GCDs and the Euclidean Algorithm (Notes 2.3.2 + 2.3.3) | ||
| Thu, Oct 5th | Lecture 13: The Euclidean Algorithm, Primes, and Factorizations (Notes 2.3.3 + 2.4) | ||
| Wed, Oct 11th | Lecture 14: Congruences and Residue Classes (Notes 2.5.1 + 2.5.2) [Updated] | ||
| Thu, Oct 12th | Lecture 15: Midterm 1 Review [Updated] | ||
| Wed, Oct 18th | Lecture 16: Residue Classes and Modular Arithmetic (Notes 2.5.1 + 2.5.2) | ||
| Thu, Oct 19th | Lecture 17: Modular Arithmetic and Inverses (Notes 2.5.2) | ||
| Mon, Oct 23rd | Lecture 18: Relations (Notes 3.1 + 3.2.1) | ||
| Wed, Oct 25th | Lecture 19: Equivalence Relations (Notes 3.2.1 + 3.2.2) | ||
| Thu, Oct 26th | Lecture 20: Partial and Total Orderings (Notes 3.3.1) - In-person lecture; no slides | ||
| Mon, Oct 30th | Lecture 21: Minimal and Maximal Elements (Notes 3.3.2) | ||
| Wed, Nov 1st | Lecture 22: Functions (Notes 3.4.1 + 3.4.2) | ||
| Thu, Nov 2nd | Lecture 23: Function Composition and Inverses (Notes 3.4.2 + 3.4.3) | ||
| Mon, Nov 6th | Lecture 24: Inverse Functions (Notes 3.4.3 + 3.4.4) | ||
| Exam Information | |||
|---|---|---|---|
| Exam | Date, Time, Location | Topics | Review Material |
| Midterm 1 Exam (sols) |
Mon, October 16th In Class |
Homeworks 1-5 Notes §1.1-2.4 |
Midterm 1 Review Problems (answers) In-class review Thu Oct 12th |
| Midterm 2 Exam (sols) |
Thu, November 16th In Class |
Homeworks 6-9 Notes §2.5-3.5.2 |
Midterm 2 Review Problems (answers) In-class review Wed Nov 15th |
| Final | Wed, December 13th 3:30 PM - 5:30 PM Churchill 103 |
The final is COMPREHENSIVE! Homeworks 1-11 Notes Chapters 1-4 |
Final Exam Review Problems (answers) Reviews Thu Dec 7th, Sat Dec 9th, Mon Dec 11th 11:45am-1:45pm in Shillman 202 |
| 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. | ||
| Read the Lecture Notes (or Textbook) | The lecture notes and the textbook are comprehensive sources 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. | ||
| Attend Problem Sessions | There are two weekly problem sessions run by the course's TAs. The goal of the problem session is to provide you a location where you can work with other students on assignments, and also get assistance from the TA. It is highly recommended to attend one of the problem sessions each week to work on the homework problems. | ||
| Use Tutoring Services | The university offers a wide variety of (free) tutoring services. Please consult the Northeastern Tutoring page for additional information on peer tutoring. Tutoring appointments can be made via MyNEU (which will provide lists of available appointments for the tutors for your specific classes); walk-in tutoring is very limited and tends to be unavailable near exam dates. | ||
| Course Schedule | |||
|---|---|---|---|
| The schedule is subject to change! All sections refer to the course lecture notes. | |||
| Week | Schedule | ||
| Week of Sep 4 (class starts 9/6) |
§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 11 | Homework #1 due Tuesday 9/12 on Canvas. §1.3.1: Sets §1.3.2: Subsets §1.3.3: Intersections and Unions |
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| Week of Sep 18 | Homework #2 due Tuesday 9/19 on Canvas. §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 25 |
Homework #3 due Tuesday 9/26 on Canvas. §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 Oct 2 | Homework #4 due Tuesday 10/3 on Canvas. §2.3: Divisibility and the Euclidean Algorithm §2.4: Primes and Unique Factorization |
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| Week of Oct 9 (no class 10/9) |
Homework #5 due Tuesday 10/10 on Canvas. §2.5: Modular Congruences and Modular Arithmetic Review for Midterm 1. |
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| Week of Oct 16 | MIDTERM 1 in class Monday 10/16 §2.5: Modular Congruences and Modular Arithmetic No homework this week. |
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| Week of Oct 23 | Homework #6 due Tuesday 10/22 on Canvas. §3.1: Relations §3.2.1: Equivalence Relations §3.2.2: Equivalence Classes §3.3: Orderings |
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| Week of Oct 30 | Homework #7 due Tuesday 10/31 on Canvas. §3.4.1: Functions §3.4.2: Function Composition §3.4.3: One-to-One and Onto Functions |
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| Week of Nov 6 | Homework #8 due Tuesday 11/7 on Canvas. §3.4.4: Bijections §3.5.1: Cardinality §3.5.2: Countable and Uncountable Sets |
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| Week of Nov 13 | Homework #9 due Tuesday 11/14 on Canvas. §3.5.2: Countable and Uncountable Sets §3.5.3: Infinite Cardinalities Review for Midterm 2. MIDTERM 2 in class Thursday 11/16 |
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| Week of Nov 20 (no class 11/22-11/26) | §5.1.1: Groups §5.1.2: Dihedral Groups No homework this week. |
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| Week of Nov 27 | §5.1.3: Symmetric Groups and Cycles §5.1.4: Subgroups and Orders §5.1.5: Cosets and Lagrange's Theorem Homework #10 due Thursday 11/30 on Canvas. | ||
| Week of Dec 4 (class ends 12/6) |
§5.2.1: Fields §5.2.2: Ordered Fields §5.2.3: The Real Numbers §5.2.3: The Complex Numbers §5.2.4: Solving Polynomial Equations Homework #11 due Thursday 12/7 on Canvas. |
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| FINAL EXAM on Wednesday 12/13, 3:30pm-5:30pm in Churchill 103 | |||