MATH 300 Fall 2018

Transition to Advanced Mathematics

Section Schedule Location
003 MWF 01:10 PM - 02:00 PM Gambrell 205

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 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.

  • In-class Tests

    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
    Each test amounts to 20% of the final grade.

  • 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.

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 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

  • 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 Non-Conditional Statements

    —If-and-Only-If 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 Non-Conditional 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