SCM101_Mathematics among the Liberal Arts_Dr. Flores.docx

Course Number: SCM 101

Course Title: Mathematics among the Liberal Arts

Instructor

Dr. Heric Flores, hflores@apostles.edu, (860) 262-2017

1. COURSE DESCRIPTION

By learning the basic ideas of game theory and other mathematical topics including geometry, algebra, calculus, probability, statistics, fractals, and symmetry, this course will allow the student to develop a creative mind that possesses critical, qualitative, and quantitative thinking skills. Students will explore mathematics through essays, exercises and puzzles which will allow them to learn key concepts organically without trepidation.

2. ENVISIONED LEARNING OUTCOMES

- Students will be able to demonstrate competency and understanding of the basic mathematical concepts.
- Students will be able to demonstrate an understanding of the mathematics they encounter in their everyday life.
- Students will be able to demonstrate their ability to identify the mathematical beauty from nature.
- Students will be able to demonstrate creativity by relating nature and mathematics

3. COURSE SCHEDULE

Every week students will be responsible for watching videos related to the current chapter, reading current chapters notes, solving simple problems and posting ideas on the discussion board. The student will write a brief summary from the videos of the current chapter. In addition to the summaries, the student has to do some simple exercises. There will be a weekly essay on a topic designed by the instructor. The essay will help you to see (first hand) the relationship between math and nature, you could visit the website https://artmathsite.wordpress.com/blog/, for examples.

Week 1: Introduction.

- What is Mathematics?
- Logic.
- Set Theory.

Readings: The instructor will provide notes related to the current chapter.

Discussion board: About the notes.

Problem set: Simple Problems and Puzzles problems.

Watch video: The videos of the week are posted on Populli

Weekly Essay.

Week 2: Numbers.

a. Natural Numbers

b. Rational Numbers

c. Integers Numbers

d. Irrational Numbers

e. Real Numbers

f. Complex Numbers

Readings: The instructor will provide notes related to the current chapter.

Discussion board: About the notes.

Problem set: Simple Problems and Puzzles problems.

Watch video: The videos of the week are posted on Populli

Weekly Essay.

Week 3: Euclidean Geometry

a. Learning the Rules of the Game: Axioms

b. Definitions and First Principals.

c. Points, Lines and Angles

d. Circle, Triangles, Squares, and Polygons.

Readings: The instructor will provide notes related to the current chapter.

Discussion board: About the notes.

Problem set: Simple Problems and Puzzles problems.

Watch video: The videos of the week are posted on Populli

Weekly Essay.

Week 4: Non-Euclidean Geometry

a. The Parallels Axiom.

b. Hyperbolic geometry

c. Elliptic geometry

Discussion board: About M.C. Escher

Problem set: Simple Problems.

Watch video: The videos of the week are posted on Populli

Weekly Essay.

Week 5: Trigonometry.

- Functions
- Trigonometric Functions and Identities.
- Functions and Geometry
- Applications of Trigonometry

Readings: The instructor will provide notes related to the current chapter.

Discussion board: Solving Practical Trigonometric and Geometric Problems.

Problem set: Simple Problems.

Watch video: The videos of the week are posted on Populli

Weekly Essay.

Week 6: Algebra

a. Definitions

b. Functions

c. Function Operations

d. Linear Functions

Readings: The instructor will provide notes related to the current chapter.

Discussion board: The Language of Algebra

Problem set: Simple Problems.

Watch video: The videos of the week are posted on Populli

Weekly Essay.

Week 7: Calculus

a. Concept of Limit

b. Differential Calculus

c. Integral Calculus

Readings: The instructor will provide notes related to the current chapter.

Discussion board: Riemann Sum

Problem set: Simple Problems.

Watch video: The videos of the week are posted on Populli

Weekly Essay.

Week 8: Midterm Exam

Week 9: Probability

a. Definitions

b. Independent and Mutually Exclusive Events

c. Basic Rules of Probability

d. Tree and Venn Diagrams

e. Applications

Readings: The instructor will provide notes related to the current chapter.

Discussion board: Probability Tree Diagram

Problem set: Simple Problems.

Watch video: The videos of the week are posted on Populli

Weekly Essay.

Week 10: Statistics

a. Definitions

b. Binomial Distribution

c. Geometric Distribution

d. Exponential Distribution

e. Normal Distribution

Readings: The instructor will provide notes related to the current chapter.

Discussion board: The Quincunx Machine.

Problem set: Simple Problems.

Watch video: The videos of the week are posted on Populli

Weekly Essay.

Week 11: Graph Theory

a. Definitions

b. Fundamental Concepts

c. Trees

d. Applications

Readings: Read the elementary notes about graph theory from the link below.

http://world.mathigon.org/Graph_Theory

Discussion board: Traveling Salesman Problem.

Problem set: Simple Problems.

Watch video: The videos of the week are posted on Populli

Weekly Essay.

Week 12: Fractals

a. Definitions

b. Fractals in Nature

c. Fractals and Technology

d. Fractal Software

Readings: The instructor will provide notes related to the current chapter.

Discussion board: Fractal Grower.

Problem set: Simple Problems.

Watch video: The videos of the week are posted on Populli

Weekly Essay.

Week 13: Fibonacci and Symmetry

a. Definitions

b. Fibonacci Numbers

c. Fibonacci in Nature

d. Symmetry

e. Symmetry in Nature

f. Group Theory

Readings: The instructor will provide notes related to the current chapter.

Discussion board: Fibonacci and Symmetry.

Problem set: Simple Problems.

Additional problems: Group Theory

Watch video: The videos of the week are posted on Populli

Weekly Essay.

Week 14: Game Theory

a. Cooperative Games

b. Nash Equilibrium

c. Nonzero Sum Games

d. Zero Sum Games

Readings: The instructor will provide notes related to the current chapter.

Discussion board: Game Theory Problem.

Problem set: Simple Problems.

Watch video: The videos of the week are posted on Populli

Weekly Essay.

Week 15: Final Exam.

4. COURSE REQUIREMENTS

- Weekly problem set– 13%
- Weekly writing: brief summary about the videos (students will grade these assignments) – 13%
- Participation on the discussion board – 13%
- Weekly Essay (students will grade these assignments) – 26%
- Midterm Exam – 10%
- Final Exam – 25%

5. REQUIRED READINGS and RESOURCES:

You could use any of the free books from below as a reference in addition to the weekly notes.

- Free PDF Geometry Book: https://archive.org/details/schoolgeometry00hall
- Free PDF Geometry Book: http://www.augusta.k12.va.us/Page/2847
- Free PDF Geometry Book: http://www.rccsd.org/HighSchool.cfm?subpage=714857
- From the website http://openstaxcollege.org/books you could download the books: Algebra and Trigonometry, Introductory Statistics, Pre-Calculus.
- Free Graph Theory Book: http://math.tut.fi/~ruohonen/GT_English.pdf
- Free Game Theory Book https://dutraeconomicus.files.wordpress.com/2014/02/joel_watson_strategy_an_introduction_to_game_theory__2013.pdf

- Weekly video links will be provided as lectures and complementary resources.

6. DISABILITIES ACCOMMODATIONS POLICY

Holy Apostles College & Seminary is committed to the goal of achieving equal educational opportunities and full participation in higher education for persons with disabilities who qualify for admission to the College. Students enrolled in online courses who have documented disabilities requiring special accommodations should contact Robert Mish, the Disability Resource Center ADA Coordinator, at rmish@holyapostles.edu or 860-632-3015. In all cases, reasonable accommodations will be made to ensure that all students with disabilities have access to course materials in a mode in which they can receive them. Students who have technological limitations (e.g., slow Internet connection speeds in convents) are asked to notify their instructors the first week of class for alternative means of delivery.

7. ACADEMIC HONESTY POLICY

Students at Holy Apostles College & Seminary are expected to practice academic honesty.

Avoiding Plagiarism

In its broadest sense, plagiarism is using someone else's work or ideas, presented or claimed as your own. At this stage in your academic career, you should be fully conscious of what it means to plagiarize. This is an inherently unethical activity because it entails the uncredited use of someone else's expression of ideas for another's personal advancement; that is, it entails the use of a person merely as a means to another person’s ends. Plagiarism includes: 1. Directly quoting without acknowledging the source. 2. Changing a few words of a text without indicating this was done and/or not acknowledging the source. 3. Not acknowledging that the structure of ideas or logic is from another author. 4. Not acknowledging a unique image (including analogies, similes, metaphors etc.) is from a particular document or author.

Students, where applicable:

· Should identify the title, author, page number/webpage address, and publication date of works when directly quoting small portions of texts, articles, interviews, or websites.

· Students should not copy more than two paragraphs from any source as a major component of papers or projects.

· Should appropriately identify the source of information when paraphrasing (restating) ideas from texts, interviews, articles, or websites.

· Should follow the Holy Apostles College & Seminary Stylesheet (available on the Online Writing Lab’s website at http://www.holyapostles.edu/owl/resources).

Consequences of Academic Dishonesty:

Because of the nature of this class, academic dishonesty is taken very seriously. Students caught plagiarizing will receive a zero for the assignment, and may be withdrawn from the class and/or expelled from Holy Apostles.

8. ATTENDANCE POLICY

Even though you are not required to be logged in at any precise time or day, you are expected to login several times during each week. Because this class is being taught entirely in a technology-mediated forum, it is important to actively participate each week in the course. In a traditional classroom setting for a 3-credit course, students would be required, per the federal standards, to be in class three 50-minute sessions (or 2.5 hours a week) and prepare for class discussions six 50-minute sessions (or 5 hours) a week. Expect to devote at least nine 50-minute sessions (or 7.5 quality hours) a week to this course. A failure on the student’s part to actively participate in the life of the course may result in a reduction of the final grade.

9. INCOMPLETE POLICY

An Incomplete is a temporary grade assigned at the discretion of the faculty member. It is typically allowed in situations in which the student has satisfactorily completed major components of the course and has the ability to finish the remaining work without re-enrolling, but has encountered extenuating circumstances, such as illness, that prevent his or her doing so prior to the last day of class.

To request an incomplete, distance-learning students must first download a copy of the Incomplete Request Form. This document is located within the Shared folder of the Files tab in Populi. Secondly, students must fill in any necessary information directly within the PDF document. Lastly, students must send their form to their professor via email for approval. “Approval” should be understood as the professor responding to the student’s email in favor of granting the “Incomplete” status of the student.

Students receiving an Incomplete must submit the missing course work by the end of the sixth week following the semester in which they were enrolled. An incomplete grade (I) automatically turns into the grade of “F” if the course work is not completed.

Students who have completed little or no work are ineligible for an incomplete. Students who feel they are in danger of failing the course due to an inability to complete course assignments should withdraw from the course.

A “W” (Withdrawal) will appear on the student’s permanent record for any course dropped after the end of the first week of a semester to the end of the third week. A “WF” (Withdrawal/Fail) will appear on the student’s permanent record for any course dropped after the end of the third week of a semester and on or before the Friday before the last week of the semester.

10. ABOUT YOUR PROFESSOR

To know more about your instructor, please click on the link below (be aware that you need to have a Holy Apostles email to access the website).

https://sites.google.com/a/holyapostles.edu/hacs-physics-class/