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	Module R	Order of Operations	Basic mathematical symbols and terminology Basic arithmetic skills Basic understanding of order of operations	Review of: PEMDAS
Week 1	Module R	Simplifying Radicals	Basic mathematical symbols and terminology Basic understanding of Order of Operations (Module R) Basic understanding of exponents and radicals Basic understanding of factoring polynomials and definition of a factor Understanding operations with fractions	Review the following radical expression concepts: evaluate square roots use the product rule to simplify square roots use the quotient rule to simplify square roots add and subtract square roots
Week 1	Module R	Simplifying Exponents	Basic mathematical symbols and terminology Basic arithmetic skills Basic understanding of Order of Operations (Module R) Basic understanding of exponents	Review the following rules of exponents: product rule quotient rule power rule zero exponent rule negative rule Review how to find the power of a product and a quotient Review how to simplify exponential expressions
Week 1	Module R	Factoring Polynomials	Basic mathematical symbols and terminology Basic arithmetic skills Basic understanding of Order of Operations (Module R) Basic prime factorization Basic understanding of factoring	Review factoring techniques for the following type of polynomials: factor the greatest common factor of a polynomial factor a trinomial factor by grouping factor a perfect square trinomial factor a difference of squares
Week 1	Module R	Solving Equations	Basic mathematical symbols and terminology Basic arithmetic skills Basic understanding of Order of Operations (Module R) Basic understanding of factoring	Review the following linear equation topics: Basic mathematical symbols and terminology solving linear equations in one variable finding a linear equation write and interpret a linear equation
Week 1	Module R	Solving Inequalities	Basic mathematical symbols and terminology Basic arithmetic skills Basic understanding of Order of Operations (Module R) Basic understanding of factoring	Review the following linear inequality topics: use interval notation use properties of inequalities solve inequalities in one variable algebraically
Week 1	Module R	Linear Equations	Basic mathematical symbols and terminology Basic arithmetic skills Basic understanding of Order of Operations (Module R) Basic understanding of factoring Basic understanding of Solving Equations (Module R)	Solving and constructing Linear Equations
Week 1	Module R	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 R) Understanding of the Cartesian coordinate system	Being able to graph a Linear Equations
Week 2	Module 1.1	Functions	Basic understanding of Linear Equations (Module R) Basic understanding of Equations (Module R)	Determine whether a relation represents a function.
Week 2	Module 1.1	Function Notation	Basic understanding of Linear Equations (Module R) Basic understanding of Equations (Module R) Basic understanding of Graphs (Module R)	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 2	Module 1.2	Domain of a Function	Basic understanding of interval notation (Module R: Solving Inequalities)	Find the domain of a function defined by an equation. Graph piecewise-defined functions.
Week 2	Module 1.2	Range of a Function	Basic understanding of interval notation (Module R: Solving Inequalities)	Find the domain of a function defined by an equation. Graph piecewise-defined functions.
Week 2	Module 1.2	[Toolkit Functions]]	Basic understanding of Cartesian coordinate system (Module R: Graphs) Basic understanding of interval notation (Module R: Solving Inequalities)	Identify the basic toolkit functions Determine Domain and Range for the basic toolkit functions (Module 1.2) Graph the basic toolkit functions. (Module R)
Week 3	Module 2.1	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 1). 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 1). The student can substitute values for variables in an Equations and solve for an unknown (Module R)	Identify power functions. Identify end behavior of power functions. Identify polynomial functions. Identify the degree and leading coefficients of polynomial functions.
Week 3	Module 2.1	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 1). 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 1). The student can substitute values for variables in an Equations and solve for an unknown (Module R).	Identify polynomial functions. Identify the degree and leading coefficients of polynomial functions.
Week 3	Module 2.2	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 4	Module 3.1	Dividing Polynomials	Basic understanding of multiplying and dividing fractions. Basic understanding of simplifying fractions by common factors. Basic understanding of the rules of exponents. (Module R: Simplifying Exponents) Basic understanding of Factoring Polynomials (Module R)	Use long division to divide polynomials Use synthetic division to divide polynomials
Week 4	Module 3.2	Zeros of Polynomials	Basic understanding of multiplying and dividing fractions. Basic understanding of simplifying fractions by common factors. Basic understanding of Factoring Polynomials (Module R) Basic understanding of Functions (Module 1.1) Basic understanding of Solving Equations (Module R)	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 5	Module 4.1	More on Polynomial Functions	The student understands that zero in the denominator of a fraction is undefined. Basic understanding of Polynomial Functions The student recalls the Graphs and equations of Toolkit Functions, and their associated Domain and Range (Module 1.2 & R).	Solving applied problems involving Polynomial Functions. Use arrow notation.
Week 5	Module 4.2	Rational Functions	Rational Expressions. 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 1.2 & R).	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 6	Module 5.1	Graphs of Polynomials	Basic understanding of Graphs (Module R) Basic understanding of Polynomial Functions (Module 2.1)	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 6	Module 5.2	Graphs of Rational Functions	Basic understanding of Graphs (Module R) Basic understanding of Rational Functions (Module 4.1)	Identify and graph vertical asymptotes Identify and graph horizontal asymptotes Determine behavior of rational functions around vertical asymptotes Graph rational functions
Week 7	Module 6	Transformations of Functions	Understanding of Functions (Module R) Understanding of Function Notation (Module R)	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 8	Module 7.1	Composition of Functions	Understanding of Function Notation (Module R) Understanding of Functions (Module R)	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 8	Module 7.2	Inverse Functions	Understanding of Function Notation (Module R) Understanding of Functions (Module R) 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 9	Module 8.1	Exponential Functions	Understanding the Toolkit Functions for exponential functions (Module 1) Understanding the Domain and Range for exponential functions (Module 1) Understanding of Simplifying Exponents (Module R)	Evaluate exponential functions. Find the equation of an exponential function. Use compound interest formulas. Evaluate exponential functions with base e.
Week 9	Module 8.2	Logarithmic Functions	Understanding the Toolkit Functions for logarithmic functions Understanding the Domain and Range for logarithmic functions (Module 1) Difference between Linear and Exponential Functions (Module R & 8.1)	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 10	Module 9.1	Logarithmic Properties	Understanding how to convert between logarithm and exponential forms. (Module 8.1 & 8.2) Understanding Order of Operations. (Module R) Understanding of Simplifying Exponents (Module R)	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 10	Module 9.2	Exponential Equations	Understanding rules for solving Linear Equations (Module R) Understanding how to check a solution to an equations (Module R) Understanding rules for solving Quadratic Equations (Module 2.1) Understanding of Logarithmic Properties (Module 9.1)	Use like bases to solve exponential equations. Use logarithms to solve exponential equations.
Week 10	Module 9.2	Logarithmic Equations	Understanding rules for solving Linear Equations (Module R) Understanding how to check a solution to an equations (Module R) Understanding rules for solving Quadratic Equations (Module 2.1) Understanding of Logarithmic Properties (Module 9.1)	Use the definition of a logarithm to solve logarithmic equations. Use the one-to-one property of logarithms to solve logarithmic equations. Solve applied problems involving exponential and logarithmic equations.
Week 11	Module 10	Exponential Models	Understanding of Simplifying Exponents (Module R) Understanding of Exponential Functions (Module 8.1) Understanding of Exponential Equations (Module 9.2)	Model exponential growth and decay Use Newton's Law of Cooling Choose an appropriate model for data Express an exponential model in base e
Week 11	Module 10	Logarithmic Models	Understanding of Logarithmic Functions (Module 8.2) Understanding of Logarithmic Properties (Module 9.1) Understanding of Logarithmic Equations (Module 9.2)	Use logistic-growth models Choose an appropriate model for data
Week 12	Module 11	Modeling using Variation	Understanding of Simplifying Exponents (Module R) Understanding of Exponential Functions (Module 8.1) Understanding of Logarithmic Functions (Module 8.2) Understanding of Logarithmic Properties (Module 9.1) Understanding of Exponential Equations (Module 9.2) Understanding of Logarithmic Equations (Module 9.2) Understanding of Exponential (Module 10) Understanding of Logarithmic Models (Module 10)	Solve direct variation problems Solve inverse variation problems Solve problems involving joint variation
Week 13	Module 12.1	Systems of Equations in Two Variables	Solving and Graphing linear equations in 2 variables. (Module R) Understanding Order of Operations (Module R)	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 13	Module 12.2	Systems of Equations in Three Variables	Solving Systems of Equations in Two Variables (Module 12.1)	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