Math 1365 (Introduction to Mathematical Reasoning, Course #17582), Fall 2019
| Course Information | |||||
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| Instructor | Class Times | Office Hours | |||
| Evan Dummit edummit at northeastern dot edu |
MWR 9:15am-10:20am, Hastings Suite 205 | MR 10:45am-12:15pm MR 3:00pm-4:00pm 571 Lake Hall |
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| 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.) | |||||
| All homework assignments will be posted on this webpage (see below). | |||||
| The instructor will write lecture notes for the course (see below) to supplement the official textbook as the semester progresses. The course will follow the presentation in E. Scheinerman's "Mathematics: A Discrete Introduction", but it is not necessary to purchase the textbook for this course. | |||||
| 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 Mon Sep 16th. (solutions)
Homework #2, due Mon Sep 23rd. (solutions) Homework #3, due Mon Sep 30th. (solutions) Homework #4, due Wed Oct 9th. (solutions) Homework #5, due Wed Oct 16th. (solutions) Homework #6, due Mon Oct 28th. (solutions) Homework #7, due Wed Nov 6th. (solutions) Homework #8, due Wed Nov 13th. (solutions) Homework #9, due Wed Nov 20th. (solutions) Homework #10, due Wed Dec 4th. (solutions) | |||||||
| Handouts / Lecture Notes | |||
|---|---|---|---|
| Handout | Topics | ||
| Chapter 1: Proofs, Logic, and Sets (28pp, v1.00, updated 9/22) (changes in 1.00: added basic subsets proposition to 1.3.2, added 1.4.3-1.4.4) (changes in 0.70: added 1.4) |
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 (19pp, v1.00, 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 (23pp, v1.02, updated 11/6) (changes in 1.02: fixed minor typos and chapter numbering) (changes in 1.00: added 3.5, added minor comments in 3.4) |
3.1 ~ Relations 3.2 ~ Equivalence Relations 3.3 ~ Orderings 3.4 ~ Functions 3.5 ~ Bijections and Cardinality |
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| Chapter 4: Counting Principles (23pp, v1.00, updated 11/21) (updates in 1.00: fixed typo in 4.1.3, added 4.2-4.3, moved derangements from 4.1.4 to 4.3.2) |
4.1 ~ Enumeration Techniques (Permutations, Combinations, Binomial Coefficients, Inclusion-Exclusion, Counting With Repetition) 4.2 ~ The Pigeonhole Principle (Statements, Examples) 4.3 ~ Other Counting Problems (Prime Powers in Factorials, Derangements, Counting Equivalence Relations, Multinomial Theorem, Stirling Numbers) |
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| Exam Information | |||
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| Exam | Date, Time, Location | Topics | Review Material |
| Midterm 1 (Exam), (Solutions) |
Thu, October 17th In Class |
Homeworks 1-5 Notes Chapters 1-2 |
Review Problems, answers In-class review Wed Oct 16th |
| Midterm 2 (Exam), (Solutions) |
Wed, November 20th In Class |
Homeworks 6-9 Notes Chapter 3 + 4.1.1-4.1.5 |
Review Problems, answers In-class review Mon Nov 18th |
| Final (Definition Sheet) |
Mon, December 9th 10:30am-12:30pm 411 Ell Hall |
The final is COMPREHENSIVE! Homeworks 1-10 Notes Chapters 1-4 |
Review Problems, answers In-class review Mon Dec 2nd In-class review Wed Dec 4th |
| Bring your University ID to all exams. Cell phones, electronic or calculating devices, books, and notes of any kind will NOT be permitted in exams. | |||
| Tips For Success In This Course | |||
|---|---|---|---|
| Attend Lecture | Missing lecture is a bad idea! If for any reason you cannot make it to a class, you should 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 optional weekly problem sessions run by the course's TA. These sessions are held on Tuesdays in 553 Lake Hall from 5:00pm-6:00pm and from 6:00pm-7:00pm. 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 the TA. | ||
| 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 | |||
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| 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 No homework this week. |
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| Week of Sep 9 | §1.2.2: Boolean Operators and Boolean Logic §1.3.1: Sets §1.3.2: Subsets §1.3.3: Intersections and Unions No homework this week. |
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| Week of Sep 16 | Homework #1 due Monday 9/16 at 4pm. §1.3.3: Intersections and Unions §1.3.4: Complements and Universal Sets §1.3.5: Cartesian Products §1.4.1: Variables and Quantifiers |
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| Week of Sep 23 |
Homework #2 due Monday 9/23 at 4pm. §1.4.2: Properties of Quantifiers §1.4.3: Indexed Sets §2.1: The Integers, Axiomatically §2.2.1: Induction |
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| Week of Sep 30 |
Homework #3 due Monday 9/30 at 4pm. §2.2.2: Examples of Induction §2.3: Divisibility and the Euclidean Algorithm §2.4: Primes and Unique Factorization |
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| Week of Oct 7 | Homework #4 due Monday 10/7 at 4pm. §2.4: Primes and Unique Factorization §2.5: Modular Congruences and Modular Arithmetic |
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| Week of Oct 14 (no class 10/14) |
Homework #5 due Wednesday 10/16 at 4pm. Review for Midterm 1. MIDTERM 1 in class Thursday 10/17 |
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| Week of Oct 21 | §3.1: Relations §3.2: Equivalence Relations §3.3: Orderings No homework this week. |
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| Week of Oct 28 | Homework #6 due Monday 10/28 at 4pm. §3.4: Functions §3.5: Bijections and Cardinality |
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| Week of Nov 4 | Homework #7 due Monday 11/4 at 4pm. §3.5.1: Bijections, Cardinality §3.5.2: Countable and Uncountable Sets §3.5.3: Infinite Cardinalities §4.1.1: Addition and Multiplication Principles |
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| Week of Nov 11 (no class 11/11) |
Homework #8 due Wednesday 11/13 at 4pm. §4.1.2: Permutations and Combinations §4.1.3: Binomial Coefficients and the Binomial Theorem §4.1.4: Inclusion-Exclusion §4.1.5: Counting With Repetition |
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| Week of Nov 18 | Homework #9 due Monday 11/18 at 4pm. Review for Midterm 2. MIDTERM 2 in class Wednesday 11/20 §4.1.6: Additional Counting Problems §4.2: The Pigeonhole Principle |
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| Week of Nov 25 (no class 11/27-12/1) |
§4.3: Other Examples of Counting Problems No homework this week. | ||
| Week of Dec 2 (class ends 12/4) |
Review for Final Exam Homework #10 due Wednesday 12/4 at 4pm. |
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| FINAL EXAM Mon December 9th, 10:30am-12:30pm, location TBA | |||