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

Calculus II
(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:

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.

Exploratory Sessions
There will be eigth inclass 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.

Inclass Tests
There are three inclass tests, initially scheduled as follows:
 Test #1: Monday, October 8th
 Test #2: Monday, October 22nd
 Test #3: Monday, November 19th

Final Exam
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
 Weatherrelated 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

Honor Code
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.
Learning Outcomes
The emphasis in most upperlevel 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 prooforiented 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 problemsolving.
 Improvement of communication in mathematics.
 Understanding the nature of mathematics and its language.
Lesson Plan

Fri, Aug 24
Review of Course content, policies, etc.

Mon, Aug 27
Sets
—Introduction to Sets
HW Assignment: Page 7. Problems 1—52

Wed, Aug 29
Sets
—The Cartesian Product
HW Assignment: Page 10. Problems 1—20

Fri, Aug 31
Sets
—Subsets
—Power Sets
HW Assignment:
—Page 14. Problems 1—16.
—Page 16. Problems 1—20

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

Fri, Sep 7
Sets
—Indexed Sets
HW Assignment: Page 28. Problems 2—4,6—8,10—14

Mon, Sep 10
Exploratory Session
(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)
Logic
—Statements
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)
Logic
—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
Logic
—Conditional Statements
—Biconditional Statements
HW Assignment:
—Page 44. Problems 1—13
—Page 46. Problems 1—5

Fri, Sep 21
Logic
—Truth Table for Statements
—Logical Equivalence
HW Assignment:
—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
Logic
—Quantifiers
HW Assignment: Page 53. Problems 1—10

Fri, Sep 28
Logic
—Translating English to Symbolic Logic
HW Assignment: Page 57. Problems 1—13

Mon, Oct 1
Exploratory Session
(Assignments #10,11 due today)

Wed, Oct 3
Logic
—Negating Statements
HW Assignment: Page 60. Problems 1—12

Fri, Oct 5
Direct Proofs
—Theorems
—Definitions
—Introduction to Direct Proofs
No HW today

Mon, Oct 8
Test #1. Sets, Logic
(Assignment #12 due today)

Wed, Oct 10
Direct Proofs
—Further Insight into Direct Proofs
—Using Cases
HW Assignment: Page 100. Problems 1—28

Fri, Oct 12
Direct Proofs
—Further Insight into Direct Proofs
No HW today

Mon, Oct 15
Mathematical Writing
No HW today

Wed, Oct 17
Exploratory Session
(Assignment #13 due today)

Mon, Oct 22
Test #2.
—Direct Proofs

Wed, Oct 24
Contrapositive Proofs
HW Assignment: Page 110. Problems 1—17

Fri, Oct 26
Proofs by Contradiction
HW Assignment: Page 118. Problems 1—24

Mon, Oct 29
Exploratory Session
(Assignments #14,15 due today)

Wed, Oct 31
Proving NonConditional Statements
—IfandOnlyIf Proofs
—Existence Proofs
—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
Exploratory Session

Wed, Nov 7
Disproof
—Counterexamples
—Disproving Existence Statements

Fri, Nov 9
Mathematical Induction
—Proof by Strong Induction

Mon, Nov 12
Exploratory Session

Wed, Nov 14
Mathematical Induction
—Proof by Smallest Counterexample

Fri, Nov 16
Review for Test #2

Mon, Nov 19
Test #2.
—Contrapositive Proof
—Proof by Contradiction
—Proving NonConditional Statements
—Proofs Involving Sets
—Disproof
—Mathematical Induction

Mon, Nov 26
Relations
—Properties of Relations

Wed, Nov 28
Relations
—Equivalence of Relations
—Equivalence Classes and Partitions

Fri, Nov 30
Functions

Mon, Dec 3
Functions
—Injective and Surjective Functions

Wed, Dec 5
Functions
—Inverse Functions

Fri, Dec 7
Cardinality
—Sets with Equal Cardinalities