College Algebra (Math 140) is essentially a "grammar course" which supports those fields which use the language of mathematics--as such the course was designed primarily to support the Bachelor of Science degree. College Algebra serves as a prerequisite for the Calculus 160 and Statistics 210 courses. (Math 140 is not sufficient for Calculus 251 which requires the trigonometry in Math 170 or Math 185.)

Many degree programs at UTM (especially those in the Bachelor of Arts programs) now require a single college-level mathematics course. Traditionally students have used College Algebra as that single course, but it may not be the best choice for them!

The course: The Nature of Mathematics (Math 130) was designed for these non-science majors. Its goal is to provide insight into what mathematics is, what mathematics attempts to accomplish, and how mathematics is used to solve real life problems. Rather than study the grammar of mathematics (algebra), we instead survey some of its literature. It is not meant to be "easier," but rather more appropriate for students who are only required to take a single mathematics course.

**Mathematics 130**

**The Nature of Mathematics**

**1. Logic: ** history, syllogisms, symbolic logic, truth tables, Venn diagrams, inductive vs. deductive reasoning, analyzing the validity of an argument

**2. Sets and Counting:** symbolic logic applied to sets, applications of Venn diagrams, elementary combinatorics, cardinality, infinite sets

**3. Probability:** history and basic terms defined using sets, conditional probabilities, independence, trees, expected value

**4. Finance:** simple vs. compound interest, present and future value, comparing annual yields, annuities, loans, how to make an amortization table

**5. Geometry:** history, early Egyptian and Greek approaches, Euclidean and non-Euclidean geometries, lengths, areas, volumes, cross-sections

**Mathematics 140**

**College Algebra**

**1. Functions:** Relations and ordered pairs, domain and range, graphing in the Cartesian Coordinate System, composite functions, inverse functions, modeling

**2. The Fundamental Theorem of Algebra:** polynomial and rational functions, zeros of a function, synthetic division, Remainder, Factor and Rational Roots Theorems, complex roots of equations, *The Fundamental Theorem of Algebra*

**3. Growth and Decay:** properties of exponents and logarithms, the base e, exponential and logarithmic functions, modeling growth and decay, solving exponential and logarithmic equations

**4. Solving Simultaneous Systems: **graphing systems of equations, using substitution, elimination, row operations on a matrix, elementary matrix operations, determinants, inverse matrices, systems of inequalities and linear programming

**5. Other:** partial fraction decompositions for a rational functions, sum and product of matrices, using technology to fit curves to points in the *xy*-plane

For more specific information, you may read the syllabi

Course Descriptions

See mathematics and statistics courses' descriptions

Courses Syllabi

See mathematics and statistics courses' syllabi