Mathematics Course Descriptions

MTH 098: Introductory Algebra, 4 credits

This course will include the topics of introductory algebra starting with a brief review of basic operations with signed integers, fractions, and decimals.   Students will learn how to solve linear equations and inequalities in one variable, how to simplify expressions with positive and negative integer exponents, how to graph linear equations and inequalities in two variables, and how to simplify algebraic expressions using the laws of exponents. The concept of function will be introduced and developed throughout the algebra sequence. Students will begin to develop problem solving techniques that require mathematical models.  This course does not fulfill the core mathematics requirement. Prerequisite: ACT math score of 19 or lower. Students may challenge their placement during orientation.

Goals And Objectives
By the end of this course, Northwood wants students to:

1. Add, subtract, multiply and divide signed integers, fractions and decimals.
2. Apply the principles, concepts and notation of ratio, proportion and percents.
3. Use the correct order of operations when evaluating algebraic expressions.
4. Translate verbal expressions into algebraic expressions.  
5. Solve linear equations and inequalities in one variable.
6. Solve a literal equation or formula for a given variable.
7. Develop a problem solving strategy. 
8. Graph linear equations in two variables by finding two points, by using the slope and a point, or by using the x- and y-intercepts.
9. Interpret the slope of the line as the rate of change.
10. Multiply, divide, and find powers of expressions with positive and negative integer exponents using the rules of exponents.
11. Add, subtract, multiply and divide polynomials.

MTH 111: Intermediate Algebra, 4 credits

This course extends the concepts, principles and skills of introductory algebra.  Students will learn how to factor polynomials, how to solve quadratic equations by factoring, how to graph linear equations in two variables, how to identify parallel and perpendicular lines, how to determine the equation of a line from the slope and a point or two points that are on the line, how to simplify radical expressions, how to write radical expressions using rational exponents, how to simplify rational expressions and how to solve rational equations.  The mathematical idea of slope as a measure of the change of a dependent variable compared to the independent variable will be explored. The concept of function will be introduced and applied to linear, rational and radical equations.  Students will recognize patterns in the graphs of these relations. Students will continue to develop problem solving strategies that require mathematical models.
Prerequisite:  ACT math score of  20-23 or earned credit for MTH 098, or successful completion of the MTH 098 Placement Examination. Students may challenge their placement during orientation before the start of fall term.

Goals And Objectives
By the end of this course, Northwood wants students to: 

1. Factor polynomials including trinomials with common factors and special products.
2. Solve quadratic equations by factoring.
3. Use function notation to express linear relations. 
4. Describe the characteristics of linear functions and interpret their slope as a constant rate of change.
5. Determine the equation of a line given the point and the slope or given two points.
6. Identify parallel and perpendicular lines by their slopes. 
7. Understand the concept of rational expressions and be able to simplify them.
8. Solve rational equations.
9. Simplify expressions with radical notation. 
10. Convert radical expressions to exponential form and vice versa and simplify them.
11. Simplify expressions with integer or rational exponents and use scientific notation.

MTH 115: College Algebra, 4 credits 

This course completes the sequence of algebraic topics necessary for a mathematically literate person.  An understanding of the Real Number System is extended to complex numbers required to solve some quadratic equations.   Students will learn how to solve quadratic equations using the quadratic formula, how to solve logarithmic and exponential equations, how to solve systems of equations in two or more variables using matrix operations, how to solve a system of linear inequalities and how to apply the notation and principles of sequences and series.  A modeling approach is used with an emphasis on functions and applied problem solving.
Prerequisite:  ACT math score of 24-28 or earned credit for MTH 111, or successful completion of the MTH 111 Placement Examination. MTH 115 is a prerequisite for MTH 231 and MTH 221 Calculus. This course is required for all students. 

Goals And Objectives
By the end of this course, Northwood wants students to:

1. Understand and use function concepts including 1-1 functions, inverses, and composition of functions.
2. Solve quadratic equations using the quadratic formula, including those with complex solutions. 
3. Use the discriminant to determine the nature of the roots of a quadratic equation.
4. Graph and identify characteristics of quadratic functions such as the vertex and axis of symmetry. 
5. Identify the solutions of a quadratic equation as the zeros of its function.
6. Use the properties of logarithms to evaluate and simplify expressions.
7. Understand the relationship between the laws of exponents and the laws of logarithms.
8. Solve exponential equations and graph exponential functions.
9. Solve problems of finance including simple and compound interest, present value and annuities.
10. Solve systems of linear equations with two or more variables by using graphs, substitution, elimination, and matrix methods.
11. Solve systems of linear inequalities in two variables. 
12. Use factorial and summation notation and apply the principles of sequences and series.

MTH 209: Intermediate Algebra, 4 credits

This course is a prerequisite for MTH 333 and every course that requires MTH 333 (Statistics I). In many other courses, such as Economics, Management, Accounting and Finance, students are expected to use mathematics skills learned in Elementary and Intermediate Algebra. Prerequisite: Mastery of prerequisite skills may be demonstrated by one or more of the following: ACT math score of 20, 21, or 22; Earned credit for MTH 100; Successful completion of the Elementary Algebra Placement Examination.

Goals And Objectives
By the end of this course, Northwood wants students to:

1. Solve systems of linear equations in two or three variables by choosing an appropriate method: graphing, elimination or substitution.
2. Solve systems of linear inequalities graphically.
3. Understand and use function notation. (Composite functions omitted for now.)
4. Simplify expressions with integer or rational exponents and use scientific notation.
5. Understand and use rational exponents and radical notation.
6. Write and simplify expressions in radical or exponential form.
7. Understand the basic concept of complex numbers as needed to solve quadratic equations.
8. Solve quadratic equations algebraically by selecting an appropriate technique including: Factoring, Finding the square roots, Completing the square, The quadratic formula, By graphing the function
9. Identify a 1-1 function and determine the inverse of the function and its graph.
10. Graph an exponential function and solve an exponential equation.
11. Understand and use the properties of logarithms.
12. Graph logarithmic functions and solve logarithmic equations.
13. Understand the relationship between logarithmic and exponential functions.
    NOTE: Appropriate technology will be included in all mathematics courses. This may be a graphing calculator, spreadsheet and other software applications and current websites.

MTH 221: Calculus, 4 credits

This course covers the basics of differential and integral calculus and its application in solving problems.  Linear and nonlinear functions are reviewed; the concepts of limits and continuity, derivatives of functions and their applications, finding maxima and minima and definite and indefinite integrals are covered. Prerequisite:  Mastery of prerequisite skills may be demonstrated by one or more of the following: ACT math score of 29 or higher, earned credit for MTH 115, or successful completion of the MTH 115 Placement Examination. This course is required by some degree programs but not all.  It meets the core requirement. It is highly recommended for any student who may apply to a master’s degree program. 

Goals And Objectives
By the end of this course, Northwood wants students to:

1. Describe linear and nonlinear functions, generate their graphs, identify zero points, understand the concept of a tangent line to a curve at a point, and be able to calculate break-even points using linear and quadratic functions.
2. Understand the concept of a limit, be able to find limits algebraically and graphically, and understand the role of limits in defining continuity and the derivative of a function.
3. Interpret the meaning of the derivative as representing instantaneous rate of change and know how to apply it for finding slope, velocity, and acceleration values, and apply it to marginal analysis.
4. Find derivatives of products and quotients using the power rule, the chain rule, and partial derivatives of 2 variables.
5. Use derivatives to find local and absolute maxima and minima, to identify concavity and inflection points, and to solve optimization problems.
6. Understand the meaning of antiderivative and be able to find antiderivatives of algebraic, exponential and logarithmic functions
7. Use indefinite and definite integral properties and formulas, including the substitution method, the Fundamental Theorem of Calculus, and integration by parts when finding the integral of a function.
8. Use integration to determine area under a curve, average value of a function over an interval and other applications such as; consumer and producer surplus, Lorenz curve, and distribution of wealth.

MTH 231: Statistics I, 4 credits

This course provides a thorough treatment of descriptive statistics; an introduction to the concepts of probability, probability distributions and sampling distributions; and an introduction to inference through estimation by confidence intervals.  Students will determine which statistical technique is appropriate depending on the data type and level of measurement, analyze the data and then interpret the results. Appropriate technology and/or software will be required.
Prerequisites: ACT score of 29 or MTH 115 and MIS 105

Goals And Objectives
By the end of this course, Northwood wants students to:

1.  Describe data types and the purpose and methods of sampling. 
2. Summarize data sets using various frequency distributions, graphs, and measures of central tendency and variation.
3. Calculate classical and empirical probabilities. 
4. Create a probability distribution and calculate its mean and standard deviation.
5. Define a discrete probability distribution and calculate the mean and the standard deviation, 
6. Understand the characteristics and applications of binomial probability distributions and calculate binomial probabilities. 
7. List the important characteristics of the normal distribution and use the standard normal probability table to determine probabilities or z-values. 
8. Understand and apply the Central Limit Theorem. 
9. Calculate a confidence interval and sample size for means and proportions.

MTH 310: College Algebra, 4 credits

The topics of this course include simplifying rational expressions; logarithmic, exponential, and polynomial functions; and solutions of equations. A modeling approach and emphasis on functions is emphasized to facilitate understanding of quantitative methods for business. Prerequisite: Mastery of prerequisite skills may be demonstrated by one or more of the following: ACT math score of 23 or higher; Earned credit for MTH 209; Successful completion of the Intermediate Algebra Placement Examination.

Goals And Objectives
By the end of this course, Northwood wants students to:

1. Understand and use functions and function notation including composite functions.
2. Solve equations using radical and fractional expressions.
3. Solve equations in quadratic form by factoring and by various methods including use of the quadratic formula.
4. Solve radical and fractional equations which result in a quadratic.
5. Understand and use complex numbers.
6. Solve inequalities involving the use of polynomials or rational expressions.
7. Graph and solve linear functions and work with various forms of the equation of a line.
8. Use the midpoint and distance formulas.
9. Solve systems of equations in three variables using calculator matrix operations.
10. Use and interpret functions of common and natural logs and write exponential equations in logarithmic form and vice versa.
11. Solve logarithmic and exponential equations.
12. Solve and graph polynomial equations.
13. Use calculator regression to model data using polynomials, logs, or exponentials and choose the best model type.
    NOTE: Appropriate technology will be included in all mathematics courses. This may be a graphing calculator, spreadsheet and other software applications and current websites.

MTH 333: Statistics I, 4 credits

This course provides an introduction to business statistics. Topics include displaying data in tables and graphs, describing data with numerical measures, concepts of probability related to discrete and continuous probability distributions, sampling distributions and confidence interval estimates. (To be replaced by MTH 231)
Prerequisites: MTH 209, MIS 105 or MIS 160

Goals And Objectives
By the end of this course, Northwood wants students to:

1. Be able to interpret data sets using various frequency distributions, graphs, measures of central tendency and dispersion.
2. Be able to calculate probabilities using classical probabilities forms and formulas.
3. Be able to count the number of possible permutations and combinations.
4. Be able to define a probability distribution, its components and calculate the mean and the standard deviation.
5. Be able to list the characteristics of the binomial probability distribution and compute probabilities for the binomial probability distribution.
6. Be able to list the important characteristics of the normal distribution and calculate probabilities using normal curve strategies.
7. Be able to determine a point beyond which a stated percent of the observations will occur, or a point beyond which there is a stated probability of occurrence.
8. Be able to describe the purposes and methods of sampling and data types.
9. Be able to interpret the central limit theorem, develop the distribution of sample means, and calculate the mean and the standard deviation.
10. Be able to compute a confidence interval and sample size for a population mean and proportion.
    NOTE: Appropriate technology will be included in all mathematics courses. This may be a graphing calculator, spreadsheet and other software applications and current websites.

MTH 334: Statistics II, 4 credits

This course is a continuation of and builds upon the concepts covered in MTH 231. It includes hypothesis testing of proportions, means and variances of one and two populations, including matched pairs. Correlation and regression, chi-square tests, and analysis of variance are also covered. Appropriate technology and/or software will be required.
Prerequisite: MTH 231; MIS 105 or MIS 160 

Goals And Objectives
By the end of this course, Northwood wants students to:

1. Develop ability to select and conduct an appropriate hypothesis test.
2. Understand and use the steps in a traditional, formal hypothesis test.
3. Test a hypothesis about a population mean using a z-test or a t-test.
4. Test a hypothesis about a population proportion using a z-test.
5. Know how to interpret a p-value and use it to test a hypothesis.
6. Test a hypothesis about two population means for independent and dependent samples.
7. Perform and interpret a one-way ANOVA to determine the equality of three or more means.  
8. Use and interpret a simple linear regression analysis.
9. Test the correlation coefficient for significance.
10. Conduct a Chi-square test for independence.

MTH 335: Quantitative Methods, 4 credits

This course covers the application of quantitative techniques to business operations, including the use of mathematical modeling in making decisions and predictions. Upon completion of the course, the student will have acquired a general knowledge of deterministic and probabilistic quantitative methods used in business including forecasting, decision theory, linear programming, network models, simulation and project management.  Appropriate technology and/or software will be required.
Prerequisite: MTH 334

Goals And Objectives
By the end of this course, Northwood wants students to:

1. Use various forecasting methods such as moving averages, exponential smoothing, trend analysis and least squares. 
2. Use various decision analysis processes in the solution of problems including expected value and decisions under uncertainty. 
3. Make a decision tree showing payoffs and analyze it. 
4. Understand the concept of linear programming and apply it to maximization and minimization problems.
5. Construct a network model for CPM and PERT systems and determine and interpret the critical path solution.