MATH 300 Fall 2018
Transition to Advanced Mathematics
|003||MWF||01:10 PM - 02:00 PM||Gambrell 205|
Click on each title for further information.
Important deadlines you need to know
|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|
|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|
(A grade of C or better in MATH 142)
...or consent from the Undergraduate Director.
Course Structure and Grading Policies
The final grade in this course will be computed as follows:
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.
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.
There are three in-class tests, initially scheduled as follows:
- Test #1: Monday, October 8th
- Test #2: Monday, October 22nd
- Test #3: Monday, November 19th
Students that have attended at least six 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:
The Honor Code applies to all work for this course. Students found violating the Honor Code will be subject to discipline.
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.
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
- 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.
Fri, Aug 24
Review of Course content, policies, etc.
Mon, Aug 27
—Introduction to Sets
HW Assignment: Page 7. Problems 1—52
Wed, Aug 29
—The Cartesian Product
HW Assignment: Page 10. Problems 1—20
Fri, Aug 31
—Page 14. Problems 1—16.
—Page 16. Problems 1—20
Wed, Sep 5
(Assignments #1—3 due today)
—Union, Intersection, Difference
—Page 18. Problems 1—10
—Page 20. Problems 1—6
—Page 23. Problems 1—14
Fri, Sep 7
HW Assignment: Page 28. Problems 2—4,6—8,10—14
Mon, Sep 10
(Assignment #4 due today)
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)
HW Assignment: Page 37. Problems 1—15
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)
—And, Or, Not.
HW Assignment: Page 41. Problems 1—14
Mon, Sep 17
Exploratory Session — The Lady or the Tiger?
(Assignments #5,6,7 due today)
Wed, Sep 19
—Page 44. Problems 1—13
—Page 46. Problems 1—5
Fri, Sep 21
—Truth Table for Statements
—Page 48. Problems 1—11
—Page 51. Problems 1—14
Mon, Sep 24
Exploratory Session — Knights and Knaves
(Assignments #8,9 due today)
Wed, Sep 26
HW Assignment: Page 53. Problems 1—10
Fri, Sep 28
—Translating English to Symbolic Logic
HW Assignment: Page 57. Problems 1—13
Mon, Oct 1
(Assignments #10,11 due today)
Wed, Oct 3
HW Assignment: Page 60. Problems 1—12
Fri, Oct 5
—Introduction to Direct Proofs
No HW today
Mon, Oct 8
Test #1. Sets, Logic
(Assignment #12 due today)
Wed, Oct 10
—Further Insight into Direct Proofs
HW Assignment: Page 100. Problems 1—28
Fri, Oct 12
—Further Insight into Direct Proofs
No HW today
Mon, Oct 15
No HW today
Wed, Oct 17
(Assignment #13 due today)
Mon, Oct 22
Wed, Oct 24
HW Assignment: Page 110. Problems 1—17
Fri, Oct 26
Proofs by Contradiction
HW Assignment: Page 118. Problems 1—24
Mon, Oct 29
(Assignments #14,15 due today)
Wed, Oct 31
Proving Non-Conditional Statements
—Existence and Uniqueness Proofs
Fri, Nov 2
Proofs Involving Sets
—How to prove \( a \in A \)
—How to prove \( A \subseteq B \)
—How to prove \( A = B \)
Mon, Nov 5
Wed, Nov 7
—Disproving Existence Statements
Fri, Nov 9
—Proof by Strong Induction
Mon, Nov 12
Wed, Nov 14
—Proof by Smallest Counterexample
Fri, Nov 16
Review for Test #2
Mon, Nov 19
—Proof by Contradiction
—Proving Non-Conditional Statements
—Proofs Involving Sets
Mon, Nov 26
—Properties of Relations
Wed, Nov 28
—Equivalence of Relations
—Equivalence Classes and Partitions
Fri, Nov 30
Mon, Dec 3
—Injective and Surjective Functions
Wed, Dec 5
Fri, Dec 7
—Sets with Equal Cardinalities