MAT1073

Course Catalog

MAT 1073. Algebra for Scientists and Engineers. (1-4) 3 Credit Hours. (TCCN = MATH 1314).

Prerequisite: Satisfactory performance on a placement examination. This course is designed to prepare the student for MAT1093 Precalculus and MAT1214 Calculus I. Topics may include algebraic expressions; equations; inequalities over the real numbers; relations; functions; polynomial and rational functions; logarithmic and exponential functions; systems of linear equations and inequalities; matrices and determinants; complex numbers; sequences; series binomial expansion; mathematical induction; permutations, and combinations. (Formerly MTC 1073. Credit can be earned for only one of the following: MAT 1073, MTC 1073, MAT1063, MTC 1023, or MAT1023. NOTE: For the purpose of the Three-Attempt Rule, these courses are considered to be equivalent and additional fees may be charged for the third or subsequent attempt to take any of these courses in any combination.) May apply toward the Core Curriculum requirement in Mathematics. Generally offered: Fall, Spring, Summer. Course Fees: LRC1 $12; LRS1 $45; STSI $21.

Topics List

Date	Sections	Topics	Prerequisite Skills	Student Learning Outcomes
Week 1	Fundamentals	Algebraic Properties	Basic mathematical symbols and terminology Basic arithmetic skills	Students will be able to correctly identify the algebraic properties: Additive & Multiplicative identity Additive & Multiplicative inverse Commutative property Associative property Distributive property Students will be able to correctly explain the algebraic properties of numbers and correctly apply these properties in procedural explanations of: Solving mathematical equations Simplifying/evaluating mathematical expressions
Week 2	Fundamentals	Fractions	Basic mathematical symbols and terminology Basic arithmetic skills Basic understanding of Algebraic Properties	Students will be able to add, subtract fractions: Determine common denominators and equivalent fractions Work with proper and improper fractions Simplify to lowest terms Students will be able to multiply, and divide fractions: Work with proper and improper fractions Simplify to lowest terms
Week 2	Fundamentals	Factoring	Basic mathematical symbols and terminology Basic arithmetic skills Basic understanding of Algebraic Properties	Students will be able to: Identify factored vs non-factored forms of a polynomial Successfully factor binomials & trinomials and difference of squares into two binomial terms Factor out GCF Multiply and / or distribute to check their factors are correct Differentiate between factors and terms of a polynomial expression
Week 3	Module 1.1	Linear Equations	Basic mathematical symbols and terminology Basic arithmetic skills Basic understanding of Algebraic Properties	Basic mathematical symbols and terminology Solving linear equations in one variable Determine a linear equation Write and interpret a linear equation Graph a linear equation
Week 3	Module 1.2	Systems of Equations in Two Variables	Basic mathematical symbols and terminology Basic arithmetic skills Basic understanding of Algebraic Properties Basic understanding of Linear Equations (Module 1.1)
Week 3	Module 0.4	Graphs	Basic mathematical symbols and terminology Basic arithmetic skills Basic understanding of order of operations Basic understanding of factoring Basic understanding of solving Linear Equations (Module 0.4) Understanding of the Cartesian coordinate system	Being able to graph a Linear Equations
Week 4	Module 1.1	Systems of Equations in Two Variables	Solving and Graphing linear equations in 2 variables. (Module 0.4)	Solve systems of equations by graphing. Solve systems of equations by substitution. Solve systems of equations by elimination Identify inconsistent systems of equations containing two variables. Express the solution of a system of dependent equations containing two variables.
Week 4	Module 1.2	Systems of Equations in Three Variables	Solving Systems of Equations in Two Variables (Module 1.1)	Solve systems of equations in three variables Identify inconsistent systems of equations containing three variables Express solutions of a system of dependent equations containing three variables
Week 5	Module 2.1	Functions	Basic understanding of Linear Equations (Module 0.4)	Determine whether a relation represents a function.
Week 5	Module 2.2	Function Notation	Basic understanding of Graphs (Module 0.4) Basic understanding of Functions (Module 2.1)	Find the value of a Functions Graph the functions listed in the library of functions. Determine whether a function is one-to-one. Use the vertical line test to identify functions.
Week 5	Module 2.2	Domain of a Function	An understanding of Solving Equations and Inequalities	Find the domain of a function defined by an equation. Graph piecewise-defined functions.
Week 5	Module 2.2	Range of a Function	An understanding of Solving Equations and Inequalities	Find the range of a function defined by an equation. Graph piecewise-defined functions.
Week 5	Module 2.2	Toolkit Functions	Basic understanding of Cartesian coordinate system (Module 0.4: Graphs)	Identify the basic toolkit functions Determine Domain and Range for the basic toolkit functions (Module 1.2) Graph the basic toolkit functions. (Module 0.4)
Week 6	Module 3.1	Intro to Power Functions	Basic understanding of power expressions. The student recalls the graphs and equations of Toolkit Functions, and their associated Domain and Range (Module 2.2). The student understands where the x-intercept and y-intercept are located given a graph. The student understands interval notation for Domain and Range (Module 2.2).	Identify power functions. Identify end behavior of power functions.
Week 6	Module 3.1	Intro to Polynomial Functions	Basic understanding of a polynomial expression. The student recalls the graphs and equations of Toolkit Functions, and their associated Domain and Range (Module 2.2). The student understands where the x-intercept and y-intercept are located given a graph. The student understands interval notation for Domain and Range (Module 2.2).	Identify polynomial functions. Identify the degree and leading coefficients of polynomial functions.
Week 6	Module 3.2	Quadratic Functions	Fundamentals of Polynomials (Module 2.1) The student understands the difference between a maximum and minimum.	Recognize characteristics of parabolas Understand how the graph of a parabola is related to its quadratic function Determine a quadratic function's minimum or maximum value Solve problems involving a quadratic function's minimum or maximum value
Week 7	Module 4.1	Dividing Polynomials	Basic understanding of multiplying and dividing fractions. Basic understanding of simplifying fractions by common factors. Basic understanding of Factoring Polynomials (Module 0.2)	Use long division to divide polynomials Use synthetic division to divide polynomials
Week 7	Module 4.2	Zeros of Polynomials	Basic understanding of multiplying and dividing fractions. Basic understanding of simplifying fractions by common factors. Basic understanding of Solving Equations and Inequalities (Module 0.3) Basic understanding of Functions (Module 1.1) An understanding of Dividing Polynomials (Module 4.1)	Evaluate a polynomial using the Remainder Theorem Use the Factor Theorem to solve a polynomial equation Use the Rational Zero Theorem to find rational zeros Find zeros of a polynomial function Solve real-world applications of polynomial equations
Week 8	Module 5.1	More on Polynomial Functions	The student understands that zero in the denominator of a fraction is undefined. Basic understanding of Polynomial Functions (Module 3.1)	Solving applied problems involving Polynomial Functions. Use arrow notation.
Week 8	Module 5.2	Rational Functions	The student understands that zero in the denominator of a fraction is undefined. The student recalls the graphs and equations of Toolkit Functions, and their associated Domain and Range (Module 2.2).	Solving applied problems involving Polynomial Functions. (Module 2.1) Use arrow notation. Solve applied problems involving rational functions. Find the Domain of rational functions. Identify vertical asymptotes. Identify horizontal asymptotes.
Week 9	Module 6.1	Graphs of Polynomials	An understanding of More on Polynomial Functions (Module 5.1)	Recognize characteristics of graphs of polynomial functions Use factoring to find zeros of polynomial functions Identify zeros and their multiplicities Determine end behavior Understand the relationship between degree and turning points Graph polynomial functions
Week 9	Module 6.2	Graphs of Rational Functions	Basic understanding of Rational Functions (Module 5.1)	Identify and graph vertical asymptotes Identify and graph horizontal asymptotes Determine behavior of rational functions around vertical asymptotes Graph rational functions
Week 10	Module 7.1	Single Transformations of Functions	Understanding of Function Notation (Module 2.1)	Graph functions using vertical and horizontal shifts Graph functions using reflections about the x-axis and the y-axis Determine whether a function is even, odd, or neither from it's graph Graph functions using compressions and stretches Combine transformations
Week 10	Module 7.2	Multiple Transformations of Functions	Understanding of Single Transformations of Functions (Module 7.1)	Combine transformations
Week 11	Module 8.1	Composition of Functions	An understanding of Multiple Transformations of Functions (Module 7.2)	Combine functions using algebraic operations Create a new function by composition of functions Evaluate composite functions Find the domain of a composite function Decompose a composite function into its component functions
Week 11	Module 8.2	Inverse Functions	An understanding of Composition of Functions (Module 7.1)	Verify inverse functions Determine the domain and range of an inverse function, and restrict the domain of a function to make it one-to-one Find or evaluate the inverse of a function Use the graph of a one-to-one function to graph its inverse function on the same axes
Week 12	Module 9.1	Exponential Properties	Understanding Order of Operations. (Module 0.1) Use the product rule for exponents. Use the quotient rule for exponents. Use the power rule for logarithms.
Week 12	Module 9.2	Exponential Functions	Understanding the Domain and Range of the Toolkit Functions for exponential functions (Module 2.2) An understanding of Exponential Properties (Module 9.1)	Evaluate exponential functions. Find the equation of an exponential function. Use compound interest formulas. Evaluate exponential functions with base e.
Week 13	Module 10.1	Logarithmic Functions	Understanding the Domain and Range of Toolkit Functions for logarithmic functions. (Module 2.2) Difference between Linear and Exponential Functions (Module 0.4 & 9.2)	Rewriting from exponential form to logarithmic form and vice versa -y=b^x\equiv\log_b(y)=x Evaluate logarithms. Use common logarithms. Use natural logarithms.
Week 13	Module 10.2	Logarithmic Properties	Understanding how to convert between logarithm and exponential forms. (Module 9.2 & 10.1)	Use the product rule for logarithms. Use the quotient rule for logarithms. Use the power rule for logarithms. Expand logarithmic expressions. Condense logarithmic expressions. Use the change-of-base formula for logarithms.
Week 14	Module 11	Modeling using Variation	Understanding of Logarithmic Properties (Module 10.2)	Solve direct variation problems Solve inverse variation problems Solve problems involving joint variation