MATH 300 Fall 2018
Transition to Advanced Mathematics
| Section | Schedule | Location | |
|---|---|---|---|
| 003 | MWF | 01:10 PM - 02:00 PM | Gambrell 205 |
Recommended Reading
Click on each title for further information.
Important deadlines you need to know
| General Dates | |
|---|---|
| Classes begin | Aug 23, 2018 |
| Labor Day Holiday | Sep 3, 2018 |
| Fall Break | Oct 18—19, 2018 |
| General Election Day | Nov 6, 2018 |
| Thanksgiving Recess | Nov 21—25, 2018 |
| Last Day of Classes | Dec 7, 2018 |
| Academic Deadlines | |
| Last Day to Change/Drop without W | Aug 29, 2018 |
| First Day W Grade Assigned | Aug 30, 2018 |
| Last Day to Drop/Withdraw without WF | Oct 15, 2018 |
| First Day WF Grade Assigned | Oct 16, 2018 |
Prerequisites
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Calculus II
(A grade of C or better in MATH 142)
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...or consent from the Undergraduate Director.
Course Structure and Grading Policies
The final grade in this course will be computed as follows:
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Homework Assignments
A set of problems is assigned at almost each standard lecture. There are initially 20 assignments planned.
Students are required to participate in the corresponding forum for each assignment. This is the best way to obtain hints and feedback.
Students must submit the required assignments in class, at the beginning of each week. Submissions must be presented in copy paper. They must be neat, legible, and properly stapled. Students are encouraged to \( \LaTeX \) their submissions, but this is not a requirement.
The combined scores of the HW amount to 20% of the final grade.
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Exploratory Sessions
There will be eigth in-class Exploratory Sessions (see Lesson Plan below for the corresponding dates).
Students are presented with an individual challenge (different assignment for different students) The individual challenge consists of one or more problems, similar to the ones posed on the assignments. Students are encouraged to use the content of their submitted assignments, as well as work in groups, to address these individual challenges.
Upon termination, each student must submit the solution to their individual challenge together with the corresponding HW assignments, if they are due on that date.
The combined scores of the Exploratory sessions amount to 20% of the final grade.
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In-class Tests
There are three in-class tests, initially scheduled as follows:
- Test #1: Monday, October 1st
- Test #2: Wednesday, October 24th
- Test #3: Monday, November 19th
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Final Exam
Students that have attended at least four Exploratory Sessions and two exams, and are unhappy with their potential final score, must notify the instructor by email on or before Monday, November 26, before 6:00 PM. Those students will have an opportunity to change their course grade by taking a (comprehensive) final exam. The score of the final exam will substitute the previous grade.
The final exam is scheduled on Friday, December 14, at 12:30 PM.
- Participation in an authorized University activity (such as musical performances, academic competitions, or varsity athletic events in which the student plays a formal role in a University sanctioned event)
- Required participation in military duties
- Mandatory admission interviews for professional or graduate school which cannot be rescheduled
- Participation in legal proceedings or administrative duties that require a student’s presence
- Death or major illness in a student’s immediate family
- Illness of a dependent family member
- Religious holy day if listed on www.interfaithcalendar.org
- Illness that is too severe or contagious for the student to attend class
- Weather-related emergencies
The course grade will be determined as follows:
| GRADE | RANGE |
|---|---|
| A | 90%-100% |
| B+ | 86%-89% |
| B | 80%-85% |
| C+ | 76%-79% |
| C | 70%-75% |
| D+ | 66%-69% |
| D | 60%-65% |
| F | below 60% |
Further Information
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Honor Code
The Honor Code applies to all work for this course. Students found violating the Honor Code will be subject to discipline.
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Student Disability Resource Center:
If you have special needs as addressed by the Americans with Disabilities Act and need any assistance, please notify the instructor immediately.
Learning Outcomes
The emphasis in most upper-level courses in mathematics is the formal development of abstract mathematical ideas. The expectation at those courses is that students will be able to read and understand proofs, and be able to construct proofs on their own in a coherent, understandable way.
This course is designed to help students transition to that level. The focus is mainly:
- Development of logical thinking skills (as in gaining the ability to think abstractly in a proof-oriented setting)
- Ability to construct and write mathematical proofs using standard methods:
- Direct Proofs
- Counterpositive Proofs
- Proofs by Contradiction
- Mathematical Induction
- Case Analysis
- Counterexamples
- Ability to read and understand written mathematical proofs.
- Development of creative thinking and problem-solving.
- Improvement of communication in mathematics.
- Understanding the nature of mathematics and its language.
Lesson Plan
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Fri, Aug 24
Review of Course content, policies, etc.
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Mon, Aug 27
Sets
—Introduction to Sets
HW Assignment: Page 7. Problems 1—52
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Wed, Aug 29
Sets
—The Cartesian Product
HW Assignment: Page 10. Problems 1—20
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Fri, Aug 31
Sets
—Subsets
—Power Sets
HW Assignment:
—Page 14. Problems 1—16.
—Page 16. Problems 1—20
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Wed, Sep 5
(Assignments #1—3 due today)
Sets
—Union, Intersection, Difference
—Complements
—Venn Diagrams
HW Assignment:
—Page 18. Problems 1—10
—Page 20. Problems 1—6
—Page 23. Problems 1—14
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Fri, Sep 7
Sets
—Indexed Sets
HW Assignment: Page 28. Problems 2—4,6—8,10—14
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Mon, Sep 10
Exploratory Session
(Assignment #4 due today)
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Wed, Sep 12 [Recording of the corresponding online session]
(Today's lesson is offered online through [webconnect] at 1 pm. Please log in as guest to join)
Logic
—Statements
HW Assignment: Page 37. Problems 1—15
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Fri, Sep 14 [Recording of the corresponding online session]
(Today's lesson is offered online through [webconnect] at 1:10 pm. Please log in as guest to join)
Logic
—And, Or, Not.
HW Assignment: Page 41. Problems 1—14
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Mon, Sep 17
Exploratory Session — The Lady or the Tiger?
(Assignments #5,6,7 due today)
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Wed, Sep 19
Logic
—Conditional Statements
—Biconditional Statements
HW Assignment:
—Page 44. Problems 1—13
—Page 46. Problems 1—5
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Fri, Sep 21
Logic
—Truth Table for Statements
—Logical Equivalence
HW Assignment:
—Page 48. Problems 1—11
—Page 51. Problems 1—14
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Mon, Sep 24
Exploratory Session — Knights and Knaves
(Assignments #8,9 due today)
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Wed, Sep 26
Logic
—Quantifiers
—Negating Statements
HW Assignment:
—Page 53. Problems 1—10
—Page 57. Problems 1—13.
—Page 60. Problems 1—12
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Fri, Sep 28
Logic
—Translating English to Symbolic Logic
No HW today
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Mon, Oct 1
Review Session
(Assignment #10 due today)
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Wed, Oct 3
Test #1. Sets, Logic
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Fri, Oct 5
Direct Proofs
—Theorems
—Definitions
—Introduction to Direct Proofs
HW Assignment: Page 100. Problems 1—28
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Mon, Oct 8
Exploratory Session
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Wed, Oct 10
Direct Proofs
—Mathematical Writing
—Further Insight into Direct Proofs
No HW today
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Fri, Oct 12
Direct Proofs
—Using Cases
—Further Insight into Direct Proofs
No HW today
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Mon, Oct 15
Direct Proofs
—Using Cases
—Further Insight into Direct Proofs
(Problems 1--11, 18, 19, 28 due today)
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Wed, Oct 17
Exploratory Session
(Problems 12--17, 20, 27 due today)
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Mon, Oct 22
Direct Proofs
—Further Insight into Direct Proofs
No HW today
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Wed, Oct 24
Test #2.
—Direct Proofs
No HW today
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Fri, Oct 26
Contrapositive Proofs
HW Assignment: Page 110. Problems 1—31
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Mon, Oct 29
Contrapositive Proofs
—Congruence of Integers
No HW today
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Wed, Oct 31
Proofs by Contradiction
HW Assignment: Page 118. Problems 1—23
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Fri, Nov 2
Proofs by Contradiction
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Mon, Nov 5
Motivational Session
(Assignments #12,13 due today)
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Wed, Nov 7
Proving Non-Conditional Statements
—If-and-Only-If Proofs
—Existence Proofs
—Existence and Uniqueness Proofs
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Fri, Nov 9
Proving Non-Conditional Statements
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Mon, Nov 12
Mathematical Induction
—Proof by Strong Induction
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Wed, Nov 14
Mathematical Induction
—Proof by Smallest Counterexample
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Fri, Nov 16
Review for Test #2
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Mon, Nov 19
Test #2.
—Contrapositive Proof
—Proof by Contradiction
—Proving Non-Conditional Statements
—Proofs Involving Sets
—Disproof
—Mathematical Induction
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Mon, Nov 26
Relations
—Properties of Relations
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Wed, Nov 28
Relations
—Equivalence of Relations
—Equivalence Classes and Partitions
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Fri, Nov 30
Functions
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Mon, Dec 3
Functions
—Injective and Surjective Functions
(Voluntary assignment #14 due today)
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Wed, Dec 5
Functions
—Inverse Functions
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Fri, Dec 7
Cardinality
—Sets with Equal Cardinalities