Math 1365 (Introduction to Mathematical Reasoning), Fall 2022
| Course Information | |||||
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| Instructor | Class Times | Office Hours | |||
| Evan Dummit edummit at northeastern dot edu |
MWR 4:35pm-5:40pm Richards 254 |
MW noon-1:00pm MWR 3:00pm-4:00pm 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.) | |||||
| Teaching Assistant | Recitation Times + Locations | Office Hours | |||
| Jose Zamora Orellana zamoraorellana.j at northeastern dot edu |
T 1:30pm--4:30pm 750 Behrakis | F 11:00am--12:30pm 141 Ryder |
By appointment 463 Lake |
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| 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) to supplement the official textbook as the semester progresses. The course will generally follow the presentation in G. Chartrand's "Mathematical Proofs: A Transition to Advanced Mathematics", but it is not necessary to purchase the textbook for this course. | |||||
| The final exam is on Tuesday December 13th from 3:30pm-5:30pm in Knowles 010. Please plan to arrive at least 5 (preferably 10) minutes early. | |||||
| 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 13th. (solutions)
Homework #2, due Tue Sep 20th. (solutions) Homework #3, due Tue Sep 27th. (solutions) Homework #4, due Tue Oct 4th. (solutions) Homework #5, due Tue Oct 11th. (solutions) Homework #6, due Tue Oct 25th. (solutions) Homework #7, due Tue Nov 1st. (solutions) Homework #8, due Tue Nov 8th. (solutions) Homework #9, due Tue Nov 15th. (solutions) Homework #10, due Thu Dec 1st. (solutions) Homework #11, due Thu Dec 8th. (solutions) | |||||||
| Handouts / Lecture Notes | |||
|---|---|---|---|
| Handout | Topics | ||
| Chapter 1: Proofs, Logic, and Sets (28pp, v2.00, posted 9/1) | 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, v2.00, posted 9/22) | 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 (22pp, v2.10, updated 10/24) (updates in v2.10: added construction of Q to end of 3.2.2, added examples to end of 3.4.4) |
3.1 ~ Relations 3.2 ~ Equivalence Relations 3.3 ~ Orderings 3.4 ~ Functions |
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| Chapter 4: Cardinality and Countability (13pp, v2.00, posted 11/3) | 4.1 ~ Cardinality and Countability 4.2 ~ The Pigeonhole Principle |
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| Chapter 5: Elements of Algebra (16pp, v1.00, posted 11/21) | 5.1 ~ Groups 5.2 ~ Fields |
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| Exam Information | |||
|---|---|---|---|
| Exam | Date, Time, Location | Topics | Review Material |
| Midterm 1 Exam (sols) |
Thu, October 13th In Class |
Homeworks 1-5 Notes §1.1-2.4 |
Midterm 1 Review Problems (answers) In-class review Wed Oct 12th |
| Midterm 2 Exam (sols) |
Thu, November 17th In Class |
Homeworks 6-9 Notes §2.5-4.1.2 |
Midterm 2 Review Problems (answers) In-class review Wed Nov 16th |
| Final | Tue, December 13th, 3:30pm-5:30pm Knowles 010 |
The final is COMPREHENSIVE! Homeworks 1-11 Notes Chapters 1-5 |
Final Supplementary Review Problems (answers) Review sessions TBA |
| 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 TA. 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. The Math Tutoring Center, located in 540B NI, is specifically set up for tutoring in mathematics courses. 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 5 (class starts 9/7) |
§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 12 | Homework #1 due Tuesday 9/13 on Canvas. §1.3.1: Sets §1.3.2: Subsets §1.3.3: Intersections and Unions |
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| Week of Sep 19 | Homework #2 due Tuesday 9/20 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 26 |
Homework #3 due Tuesday 9/27 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 3 | Homework #4 due Tuesday 10/4 on Canvas. §2.3: Divisibility and the Euclidean Algorithm §2.4: Primes and Unique Factorization |
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| Week of Oct 10 (no class 10/10) |
Homework #5 due Tuesday 10/11 on Canvas. Review for Midterm 1. MIDTERM 1 in class Thursday 10/13 |
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| Week of Oct 17 | §2.5: Modular Congruences and Modular Arithmetic §3.1: Relations No homework this week. |
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| Week of Oct 24 | Homework #6 due Tuesday 10/18 on Canvas. §3.2.1: Equivalence Relations §3.2.2: Equivalence Classes §3.3: Orderings |
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| Week of Oct 31 | Homework #7 due Tuesday 11/1 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 7 | Homework #8 due Tuesday 11/8 on Canvas. §4.1: Bijections, Cardinality §4.2: Countable and Uncountable Sets |
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| Week of Nov 14 | Homework #9 due Tuesday 11/15 on Canvas. §4.3: Infinite Cardinalities Review for Midterm 2. MIDTERM 2 in class Thursday 11/17 |
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| Week of Nov 21 (no class 11/23-11/27) | §4.4.1: The Pigeonhole Principle §4.4.2: Pigeonhole Arguments No homework this week. |
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| Week of Nov 28 | §5.1.1: Groups §5.1.2: Dihedral Groups §5.1.3: Symmetric Groups and Cycles §5.1.4: Subgroups and Orders Homework #10 due Thursday 12/1 on Canvas. | ||
| Week of Dec 5 (class ends 12/7) |
§5.1.5: Lagrange's Theorem §5.2: Fields and the Real Numbers Homework #11 due Thursday 12/8 on Canvas. |
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| FINAL EXAM on Tuesday December 13th from 3:30pm-5:30pm, Knowles 010 | |||