Yuba Community College District

Yuba College Course Outline

Course Information

Course Number: MATH 55
Full Course Title: History of Algebra
Short Title: History of Algebra
Effective Term: Spring 2017

Course Standards

Lecture Hours: 54.000
Total Units: 3.000
Total Hours: 54.00
Repeatable: No
Grading Method: Letter Grade or Pass/No Pass

Minimum Qualifications


Course Description

A history of algebra from ancient times up to the 18th century. Introduction to a variety of number systems; the operations of addition, subtraction, multiplication, and division, and the finding of square roots; sets and logic; rational, irrational, real, and complex numbers; Greek number theory; linear, quadratic, and cubic equations; and applications (including proportions, variation, compound interest, exponential growth and decay). Ideas and methods from different parts of the world and at different times are mainly presented in their historical context. This course satisfies the AA and AS degree requirement, but it does not satisfy the prerequisite for a transferable mathematics or statistics course.

Conditions of Enrollment

Completion with a C or better in: MATH 101 or MATH 101B or. Other: (Placement Exam Score)Qualifying score on the mathematics placement test. To allow the student who is prepared for Math 55 not to take the prerequisite course.

Advisories

Content

Course Lecture Content
  1. Number systems, for example
    1. Babylonian
    2. Egyptian
    3. Roman
    4. Chinese
    5. Mayan
    6. Indo-Arabic
  2. The operations as they were performed in different parts of the world at different times
    1. addition
    2. subtraction
    3. multiplication
    4. division
    5. finding of square roots
  3. Sets and logic
  4. Rational, irrational, and real numbers (including their cardinalities), and complex numbers
  5. Greek number theory
  6. Polynomial equations, including
    1. false position
    2. completing the square and the quadratic formula
    3. the cubic formula
    4. relation between roots and coefficients, zeros and factoring
  7. Applications, for example
    1. proportions using the rule of three
    2. variation
    3. compound interest
    4. exponential growth and decay


Objectives

  1. Articulate an understanding of a variety of number systems and their historical context.

  2. Perform the operations of addition, subtraction, multiplication, and division, and the finding of square roots from different parts of the world and at different times.

  3. Exhibit a rudimentary understanding of sets and logic. **Requires Critical Thinking**

  4. Demonstrate an understanding of the relation among rational, irrational, and real numbers (including their cardinalities), and complex numbers, and their historical context. **Requires Critical Thinking**

  5. In the Greek tradition, construct even and odd numbers, and figurate numbers; prove the infinitude of the prime numbers; apply Euclid's algorithm; apply Pythagoras's theorem; prove the incommensurability of the square root of 2; identify friendly numbers. **Requires Critical Thinking**

  6. Exhibit an understanding of the early appearances or historical development of the method of false position, the quadratic formula, and the cubic formula, and apply the methods to solve equations. **Requires Critical Thinking**

  7. Solve application problems. For example, proportion problems using the rule of three, and variation, compound interest, and exponential growth and decay problems. **Requires Critical Thinking**


Student Learning Outcomes

  1. Demonstrate an understanding of a variety of number systems and their historical context.
  2. Compare the ways that various peoples and cultures around the world performed the operations of addition, subtraction, multiplication, and division, and the finding of square roots.
  3. Demonstrate a rudimentary understanding of sets and logic.
  4. Demonstrate an understanding of the relation among rational, irrational, and real numbers (including their cardinalities), and complex numbers, and their historical context.
  5. Demonstrate an understanding of the Greek tradition by, a. constructing even and odd numbers, or figurate numbers; or b. proving the infinitude of the prime numbers or the irrationality of the square root of 2; or c. applying Euclid's algorithm; or d. identifying friendly numbers.
  6. Compare the ways that various peoples and cultures around the world solved linear and quadratic problems, and apply the methods to solve equations and applications.
  7. Solve application problems such as proportion problems using the rule of three, and variation, compound interest, exponential growth and decay problems.

Methods of Instruction


Assignments

Hours per week on assignments outside of the class:

Reading Assignments
Writing Assignments
Other Assignments

 

Sample Research Paper Prompts

1. There is some research that suggests that the base-60 system arose out of various mensuration systems in use.  Find out what the mensuration systems were and how they may have led to the base-60 system of ancient Babylon.

2. Describe how the Mayans reckoned time.  Compare how the Mayans reckoned time with how we reckon time.

3. In the Chinese method of double false position, the deficit is not recorded as negative, as is done in the method given in Liber Abaci, yet the solution is correct.  Compare the Chinese and European methods to determine why this is so.

 

Sample Assignment Prompts

1. The trivium and the quadrivium comprise the traditional "liberal arts" education. Write about the liberal arts and the place of mathematics in them, both historically and today. See Hardy Grant’s College Mathematics Journal articles: Mathematics and the liberal arts. Coll. Math. Journal, 30(2):96–105, March 1999; and Mathematics and the liberal arts—II. Coll. Math. Journal, 30(3):197–203, May 1999.

2. How are prime numbers used to encrypt information?

3. Research how the Chinese rod numerals have evolved and spread over time.


Methods of Evaluation


Course Materials

Textbooks:
  1. Shell-Gellasch, Amy and Thoo, J. B.. Algebra in Context, Johns Hopkins University Press, 2015, ISBN: 978-1-4214-1728-8
    Equivalent text is acceptable
Other:
  1. Scientific calculator: Texas Instruments TI-30X IIS