Course Information
Course Standards
Minimum Qualifications
 Mathematics (Masters Required)
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

Language  recommended eligibility for English 1ATo be able to read and understand the textbook. To be able to read and understand word problems.
Content
 Number systems, for example
 Babylonian
 Egyptian
 Roman
 Chinese
 Mayan
 IndoArabic
 The operations as they were performed in different parts of the world at different times
 addition
 subtraction
 multiplication
 division
 finding of square roots
 Sets and logic
 Rational, irrational, and real numbers (including their cardinalities), and complex numbers
 Greek number theory
 Polynomial equations, including
 false position
 completing the square and the quadratic formula
 the cubic formula
 relation between roots and coefficients, zeros and factoring
 Applications, for example
 proportions using the rule of three
 variation
 compound interest
 exponential growth and decay
Objectives

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

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.

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

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**

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**

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**

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
 Demonstrate an understanding of a variety of number systems and their historical context.
 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.
 Demonstrate a rudimentary understanding of sets and logic.
 Demonstrate an understanding of the relation among rational, irrational, and real numbers (including their cardinalities), and complex numbers, and their historical context.
 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.
 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.
 Solve application problems such as proportion problems using the rule of three, and variation, compound interest, exponential growth and decay problems.
Methods of Instruction

Lecture/Discussion
Assignments
Sample Research Paper Prompts
1. There is some research that suggests that the base60 system arose out of various mensuration systems in use. Find out what the mensuration systems were and how they may have led to the base60 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
 Essay/Paper
 Exams
 Homework
 Portfolio
 Problem Solving Exercises
 Quizzes
 Research Project
Course Materials

ShellGellasch, Amy and Thoo, J. B.. Algebra in Context, Johns Hopkins University Press, 2015, ISBN: 9781421417288Equivalent text is acceptable
 Scientific calculator: Texas Instruments TI30X IIS