MATH 332 – History of Mathematics

Spring 2010

 

SYLLABUS

 

COLLEGE MISSION STATEMENT

Felician College is an independent co-educational Catholic/Franciscan College founded and sponsored by the Felician Sisters to educate a diverse population of students within the framework of a liberal arts tradition.  Its mission is to provide a full complement of learning experiences, reinforced with strong academic and student development programs designed to bring students to their highest potential and prepare them to meet the challenges of the new century with informed minds and understanding hearts.  The enduring purpose of Felician College is to promote a love for learning, a desire for God, self knowledge, service to others, and respect for all creation.

 

DIVISION OF ARTS AND SCIENCES MISSION STATEMENT

The mission of the Division of Arts and Sciences is to implement and manifest the Mission of Felician College in the Programs of the Division; the General Education Program, the Developmental Educational Program, and the Core by providing the highest quality of instruction at both the undergraduate and graduate level, encouraging students to develop to their fullest potential, to gain skills for life-long learning, and to produce graduates well-equipped to contribute to society. The division achieves the stated mission by using processes of continual improvement, based upon assessment of student learning at al levels, as well as the assessment of the administrative processes and mechanisms

 

DEPARTMENT OF MATHEMATICAL SCIENCES MISSION STATEMENT

The Department of Mathematical Sciences supports the mission of Felician College by providing the portion of students’ educational experiences dealing with quantitative literacy.  The Department supports the mission of Felician College to provide a strong academic program by providing rigorous mathematics courses to students in all majors at all levels.  The Department supports the mission of the Division of Arts and Sciences by providing a high quality of instruction in mathematics at both the college level and the developmental level.  The broad variety of courses offered by the Department of Mathematical Sciences helps bring students to their highest potential by providing theory and practice related to problem solving, logical reasoning, and analytical skills.  This will help prepare Felician College students to meet future challenges with informed mathematical mind.

 

DISCLAIMER

This syllabus is subject to change according to the needs of the class as deemed appropriate by the instructor.  In case of changes, students will be notified in class and a new syllabus will be distributed.

 

Division	Arts and Sciences
Department:	Mathematical Sciences
Course Number	MATH 365R
Course level:	Undergraduate
Course Title:	Differential Equations
Instructor:	Dr. Michael Sanford, Ph.D.
Rank:	Associate Professor
Email:	sanfordm@felician.edu or msanfordphd@optonline.net
Phone:	201 559- 6000 ext. 3192
Office	Office: Room 3 Martin Hall Rutherford Campus, (or the Math Lab MH 4)

 

 

COURSE DESCRIPTION

This course is an examination of the development of mathematics. Themes include comparative mathematical systems; the origin of whole, rational, irrational, complex, and

transfinite numbers; the evolution of geometry, number theory, algebra, calculus, probability theory; and modern innovations such as chaos theory. (spring)

Prerequisite: MATH 231 or permission of instructor

 

COURSE GOALS:

The goal of this course is to open the mind of the student to where mathematics was and how it developed through time and in doing so understand how that development contributes to society as whole and to the individual as a they learn mathematics.

 

Course Objectives

·       Students will be able write and read numbers in a variety of ancient cultures and modern bases.

·       Students will be able convert numbers written in a variety ancient cultures to modern Hindu-Arabic

·       Students will be able convert from Hindu-Arabic numbers to variety ancient cultures.

·       Students will be able to read write and convert between numbers  of any modern base  to another.

·       Students will be able to do arithmetic in ancient cultures and alternate bases.

·       Students will be able to do algebra as various ancient cultures would have.

·       Students will be able to do geometry as various ancient cultures would have.

·       Understand the Pythagorean Theorem and its many proofs.

·       Understand the Golden ratio & rectangle.

·       Understand and compute the Fibonacci Sequence.

·       Students will understand how mathematics affects culture and vice versa.

·       Students will understand and do problems and proofs as past cultures and mathematicians might have done.

·       Students will understand how certain mathematicians influenced the field of mathematics.

·       Students will understand how past method can be understood in modern notations.

·       Students will understand be evaluate mathematical presentations.

·       Students will research mathematicians and their mathematics.

·      Students will be able write and read numbers in a variety of ancient cultures and modern bases.

  

TEXT: The History of Mathematics: An Introduction 6ed., David M. Burton, McGraw-Hill, ISBN 0-07-305189-6 (New at the bookstore $162.50)

 

COURSE CONTENT

Ancient Number Systems & Various Bases

Ancient Arithmetic & Various Arithmetic Algorithm

Ancients Babylonian Mathematics

Ancient Greek Mathematics

Fibonacci & Golden Ratio

Various Mathematicians and their Mathematics throughout history

 

	MONDAY	TUESDAY	WEDNESDAY	THURSDAY	FRIDAY
JAN.	18	19	20	21	22
	25	26	27	28	29
			Film:
			Story of 1
FEB.	1	2	3	4	5
			quiz		Paper 1 due
	8	9	10	11	12
	15	16	17	18	19
					Film:
					Infinite Secrets
	22	23	24	25	26
			quiz
MAR.	1	2	3	4	5
					paper 2 due
	8	9	10	11	12
SPRING
BREAK
	15	16	17	18	19
					quiz
MID-TERM	22	23	24	25	26
WEEK					Midterm
APR.	29	30	31	1	2
EASTER
BREAK
	5	6	7	8	9
			Film:
			Newton's Dark Side
	12	13	14	15	16
			quiz
	19	20	21	22	23
	26	27	28	29	30
			quiz		Film
					Brilliant Madness
MAY	3	4	5	6	7
			Flim:		Film:
			Beautiful Mind		Beautiful Mind
			Part 1		Part 2
	10	11	12	13	14
FINALS
WEEK

 

 

teaching/learning strategies

·      Class lectures, demonstrations, and discussions

·      Small group work and discussions

·      Study and homework groups

·      Individual problem solving

·      Watching DVD

·      Research and Writing Paper

 

 

grading policies

Quizzes: (25%-five quizzes @ 5% of the total grade each) Short 20 minute assessments over topics that currently being discussed in class.

Exams: (50%-two exams @ 25% of the total grade each) Midterm and Final exams will be each comprehensive.

Papers: (25%- five papers @  5% of the total grade each)

 The Story of 1 (60min) (DVD)

Discuss 1 and its pal 0? This paper is to show how well you can take in information and accurately describe the information. Write a paper in which you describe mathematically relevant information and other interesting topics.

Infinite Secrets: The Genius of Archimedes (60min) (DVD)

Mathematical Biography of Archimedes: Use the movie as a starting point and include other references, not all Internet references. You must include mathematics that is attributed to Archimedes. To achieve the best grade, you demonstrate that you have gone beyond the scope of the film and researched Archimedes’ mathematics. Choose one mathematical topic and going into detail.

Newton’s Dark Secrets: The First Modern Scientist Last ancient Magician.

 (60min) (DVD)

Mathematical Biography of Sir Isaac Newton: Use the movie as a starting point and include other references, not all Internet references. You must include mathematics/physics that is attributed to Newton. To achieve the best grade, you demonstrate that you have gone beyond the scope of the film and researched Newton’s mathematics. Choose one mathematical or physics topic and going into detail.

The Proof (60min) (DVD)  

What does it take to be a mathematician in the modern world? What did Andrew Wiles do the same and different. What did Andrew Wiles do? What is Fermat’s Last Theorem.  What are some of the results that Wiles relied on. Can we make a conclusion about whether Fermat could have proved his result.? Use the movie as a starting point and include other references, not all Internet references.

A Brilliant Madness (60 min) (DVD) & Beautiful Mind (120 min) (DVD) [in two parts] – Compare and Contrast.

Discuss fact versus fiction. Who is John Nash? What did he do? What prize did he receive and in what area of study? How does the fictional story portray what Nash’s Mathematics? Research Nash equilibrium and give your explanation. How do the two films portray or discuss Nash’s psychosis? What stressor may have led to Nash psychotic break? Use the movie as a starting point and include other references, not all Internet references.

 

 

 

GRADING RUBRICS

Mathematical Problem Solving questions:

The student gets 100% of the credit for an exam question only if the answer is correct, all work is shown, and the work shown leads to the correct answer. Partial credit is given under the following circumstances:

• If the work is substantially correct but there is a minor error in arithmetic, the student will get close to full credit (99%-75% of the credit).
• If there are some mistakes but the student has shown an understanding of at least some of the math, the student will get credit proportional to the amount of understanding demonstrated (74%-1% of the credit).
• No credit (0%) for work that is nonexistent or unrelated

Papers and Essay Questions:

 

Writing Skill	4	3	2	1	0
Content	Writing is clear focused, and contains a main idea supported by details	Writing has a limited focus main idea, and details, but that focus is still evident	Minimal development of main idea and details.	Ideas are underdeveloped and unclear.	Content is unrelated to the assigned topic or nonexistent.
Organization	The central idea develops from a thesis through clear sequencing, and order.	Sequencing present, but development may be occasionally unclear	Development present, but transitions and sequencing need more consistency.	Lack of effective sequencing and development.	No development and no sequencing.
Structure	Sentence fluency, grammatical structure, word choice, and voice support the thesis.	Writing flows but some minor errors in grammar, word choice, and voice.	Noticeable clear sentence fluency, but structural errors detract from thesis.	Unclear structure, grammatical errors that make writing confusing.	No structure or grammatical errors that make writing unreadable.
Documentation	Clear effective use of MLA or APA style. Appropriate use personal explanation of researched material, researched assertions, citation correctly done in the paper and in the bibliography.	Writing follows proper documentation and citations but paper relies too much on quotations or paraphrasing from the research and not enough of personal assertions and explanations.	Writing relies too much on paraphrase or quoted material. Documentation is correct but to little evidence of original thought or understanding.	No citations or documentation to support thesis. Writing relies almost exclusively on paraphrase or quoted material.	No citations or documentation to support thesis.

 

 

 

COURSE POLICIES

Missed Exams and Quizzes: You need to make arrangements with me to take another time.

Late papers you lose 5% every week it is late.

In class behavior, I expect you to act as the adult you are and respect your classmates and myself which means the golden rule applies.

Calculators : Anything will do. We won’t use them too much but there will be occasion.

Academic dishonesty, you are expected to work on your own unless otherwise directed. Quizzes will occasionally be a group effort.

Note: College Wide Policies can be found in the College Catalog.

 

HERE IS A QUICK REVIEW OF THINGS TO REMEMBER FWHEN WRITING A RESEARCH PAPER

 

Department of English     

Dr. George Castellitto

 

1. Choose a tentative topic based on your interest.
2. Narrow your topic based on reading of primary sources.
3. Speculate or hypothesize about a thesis.
4. Start research by studying SOURCES in the following order:

ü  Experts (e.g., your professor)

ü  Bibliographies and Indices

ü  Data Bases

ü  Reference Books

ü  Abstracts

ü  Catalogue (Card or Computer)

5. Finalize your thesis.
6. Take specific notes from your secondary sources.  Indicate in those notes the authors of your sources, page numbers of quoted material, and other relevant material.
7. Formulate your Works Cited or References page (formerly referred to as the Bibliography).
8. Make an outline. 
9. Write your First Draft.
10. Revise if necessary, and write your Second or Final Draft.
11. Use MLA format for humanities papers and APA format for sciences papers.
12. Other than common knowledge, document all material that did not originate from your intellect.

 

DOCUMENTATION FORMAT

 

Modern Language Association (MLA)

Book:

Bloom, Allan.  The Closing of the American Mind.  New York: Simon and Schuster, 1987.

Culler, Jonathan.  On Deconstruction: Theory and Criticism after Structuralism. Cornell UP, 1982.

Article from Journal:

Knowles, Frederick.  “Shades of Metaphor in the Later Poetry of Wallace Stevens.” New England Quarterly 48 (June 1993): 31-49

Essay from a collection of essays:

Harvey, W. J.  “Theme and Texture in The Great Gatsby.”  Twentieth Century Interpretations of The Great Gatsby.  Ed. Ernest Lockridge.  Englewood Cliffs:Prentice Hall, 1968.  90-100.

 

Electronic source:

 

The typical entry should include the following information:

1. Title of the source (italicized).
2. Name of the author or editor (if available).
3. Electronic publication information, including version number (edition or volume), date of electronic publication or of latest update, and name of any sponsoring institution or organization.
4. Date of access and network address.

 

 American Psychological Association (APA)

Book:

Bloom, A.  (1987).  The closing of the American mind.  New York: Simon and Schuster. Culler, J.  (1982).  On deconstruction: theory and criticism after Structuralism. Cornell University Press.

Article from journal:

Knowles, F.  (1993).  Shades of metaphor in the later poetry of Wallace Stevens.  New England Quarterly, 48, 31-49.

Parenthetical Reference (to replace footnotes and endnotes):

MLA  (Bloom 82).                   APA  (Bloom, 1987).   OR   (Bloom, 1987, pp. 71-3).

                                               

Note that period follows parenthesis.