Course Descriptions and Prerequisites

A lab designed to support students in MTH 160 (Statistics I) or MTH 162 (Statistics for the Social Sciences) at MCC. It is only for students who need MTH 160, MTH 161 or MTH 162 as the terminal mathematics course in their program and place at Mathematics Level 4, 5, or 6. It is not for students who need to take MTH 104 or MTH 165 (or higher). Topics include, but are not limited to, arithmetic operations on real numbers, solving linear equations, simplifying expressions containing whole number exponents, using a calculator to find decimal approximations of square roots, graphing linear equations, and appropriate applications of these topics. MTH 060 is a developmental course. It does not fulfill a mathematics requirement.

Prerequisite(s): TRS 094 with a minimum grade of C OR MCC Level 4 Mathematics Placement and ENG 101 OR ENG 200 OR English Placement. Co-Requisite(s): MTH 160 or MTH 162

Course Learning Outcomes
1. Evaluate an expression by applying the priority of operations.
2. Solve first degree equations in one variable.
3. Solve literal equations
4. Simplify expressions involving whole number exponents.
5. Graph linear equations on the Cartesian coordinate system.
6. Solve applications involving linear equations.
7. Use interval notation to express linear inequalities in one variable.
8. Determine the domain and range of functions.
9. Evaluate a function for a specified input value.

A support course designed to reinforce Intermediate Algebra skills for students in MTH 165 (College Algebra). Topics to be covered include, but are not limited to, reviewing factoring techniques, simplifying polynomial, complex number, rational, radical and exponential expressions; and solving quadratic, rational and literal equations. MTH 065 is typically taken with specially designated sections of MTH 165. MTH 065 is a developmental course. It does not fulfill a mathematics requirement

Pre-requisite(s): MCC Level 7 Mathematics placement, MTH 104 with a grade of C- or higher, or permission of instructor. Co-requisite(s): MTH 165

Course Learning Outcomes
1. Factor polynomials.
2. Solve quadratic equations.
3. Solve rational equations.
4. Simplify rational expressions, complex numbers, or radical expressions.
5. Simplify expressions involving rational exponents.
6. Solve literal equations for a single variable.
7. Solve compound linear inequalities in one variable.
8. Evaluate functions using function notation.

A basic algebra course designed to prepare students for MTH 160 (Statistics I) or MTH 162 (Statistics for the Social Sciences) at MCC. It is only for students who need MTH 160, MTH 161 or MTH 162 as the terminal mathematics course in their program and place at Mathematics Level 4, 5, or 6. It is not for students who need to take MTH 104 or MTH 165 (or higher). Topics include, but are not limited to, arithmetic operations on real numbers, solving linear equations and inequalities, simplifying expressions containing integer exponents, simplifying square roots and finding decimal approximations, graphing linear equations, an introduction to function notation, and appropriate applications of these topics. MTH 096 is a developmental course. It does not fulfill a mathematics requirement.

Prerequisite(s): MCC level 4 mathematics placement or higher or TRS 094 with a grade of C or better.

Course Learning Outcomes
1. Evaluate an expression by applying the priority of operations.
2. Solve first degree equations in one variable.
3. Solve literal equations.
4. Simplify expressions involving integer exponents.
5. Graph linear equations on the Cartesian coordinate system.
6. Solve applications involving linear equations.
7. Use interval notation to express linear inequalities in one variable.
8. Solve and graph linear inequalities in one variable.
9. Determine the domain and range of functions written as a correspondence or a set of ordered pairs.
10. Determine the domain and range of functions graphically.
11. Evaluate a function, expressed in function notation, for a specified input value.
12. Interpret linear models.

An introductory mathematics course designed to develop algebraic skills. Topics include, but are not limited to: solving linear equations and inequalities, performing arithmetic operations on polynomials, simplifying expressions containing integer exponents, graphing linear equations, and solving systems of two linear equations.

Prerequisite: TRS 094 with a grade of C or better, or MCC Level 4 Mathematics Placement.

Course Learning Outcomes
1. Perform arithmetic operations on polynomials.
2. Evaluate an expression by applying the priority of operations.
3. Solve first degree equations in one variable.
4. Solve literal equations.
5. Simplify expressions involving integer exponents.
6. Graph linear equations on the Cartesian coordinate system.
7. Solve systems of linear equations in two variables.
8. Solve applications involving linear equations.
9. Solve linear inequalities in one variable.

An accelerated version of MTH 098, intended for students who need a review of basic algebra content. Topics to be covered include, but are not limited to, reviewing arithmetic operations on rational numbers, solving linear equations, graphing on the Cartesian Coordinate system and factoring polynomials. MTH 099 is typically taken with specially designated sections of MTH 104. MTH 099 is a developmental course. It does not fulfill a mathematics requirement.

Prerequisite(s): MCC level 5 mathematics placement OR TRS 094 with a minimum grade of A, OR MTH 096 with a minimum grade of B-, OR MTH 098 with a minimum grade of C-, OR MTH 152 with a minimum grade of C OR permission of instructor.

Course Learning Outcomes
1. Perform arithmetic operations on polynomials.
2. Evaluate an expression by applying the priority of operations.
3. Solve first degree equations in one variable.
4. Solve literal equations.
5. Factor polynomials.
6. Solve quadratic equations by factoring.
7. Simplify expressions involving integer exponents.
8. Graph linear equations on the Cartesian coordinate system.
9. Solve systems of linear equations in two variables.
10. Solve applications involving linear equations.
11. Solve and graph linear inequalities in one variable.
12. Graph linear inequalities in two variables.

An intermediate mathematics course designed to further develop algebraic skills. Topics include, but are not limited to: factoring polynomials; solving equations involving quadratic, rational, and radical expressions; performing arithmetic operations on rational expressions, complex numbers, and radical expressions; evaluating functions; graphing quadratic functions; and simplifying expressions involving rational exponents; appropriate applications of topics.

Prerequisite: MTH 098 with a grade of C or better, or MTH 099 with a grade of C or better, or MCC Level 6 Mathematics Placement.

Course Learning Outcomes
1. Solve quadratic equations.
2. Solve rational equations.
3. Solve radical equations.
4. Factor polynomials.
5. Perform arithmetic operations on rational expressions.
6. Perform arithmetic operations on complex numbers.
7. Perform arithmetic operations on radical expressions.
8. Evaluate functions using function notation.
9. Graph quadratic equations.
10. Simplify expressions involving rational exponents.
11. Solve applications involving quadratic equations.
12. Solve applications involving rational equations

This course will cover the basic concepts and processes of mathematics applied to various business situations including statistical procedures, percentage and percent distributions of financial statement data, merchandising, payrolls, taxation and insurance. Other topics include simple interest, compound interest and annuities. MTH 130 is a course for career business.

Prerequisite(s): MCC Level 2 Mathematics placement.

Course Learning Outcomes
1. Solve percent problems.
2. Solve payroll problems.
3. Compute the net cost of merchandise after a commercial discount.
4. Compute various retail measures such as cost, selling price, markup, markdown, or break even amount.
5. Solve applied problems pertaining to simple interest.
6. Solve applied problems pertaining to compound interest.
7. Solve consumer loan problems.
8. Solve applied problems pertaining to property taxes.
9. Solve applied problems pertaining to insurance premiums.
10. Analyze financial statements.
11. Interpret graphs.
12. Compute statistical measures.

A study of various topics including an introduction to estimation, algebra, geometry, consumer mathematics, probability and statistics, with an emphasis on critical thinking and interpreting results. Other topics may be covered at the discretion of the instructor.

MTH 150 is a common selection by Liberal Arts students with fewer than three years of high school mathematics. MTH 150 is not a prerequisite course for MTH 160 or higher. Although this course can satisfy your mathematics requirement for some MCC programs and transfer to some baccalaureate institutions, if you are planning to transfer please speak with an academic advisor or Career and Transfer to ensure that this course meets your goals.

Prerequisite: TRS 094 with a grade of C or better, or MCC Level 4 Mathematics placement.

Course Learning Outcomes
1. Use estimation to approximate an answer.
2. Use geometric formulas to solve applied problems using unit conversions where necessary.
3. Compute interest for common loans.
4. Compute interest rates for common loans.
5. Compute payments for common loans.
6. Compute probabilities, odds, or expected value.
7. Interpret results from probability based calculations.
8. Interpret standard statistical graphs.
9. Calculate simple descriptive statistics for a given set of data.
10. Use common properties of a normal distribution to draw basic conclusions about the underlying data

A course focused on mathematical concepts needed to solve problems in technical areas. Topics include, but are not limited to: measurements; geometry; exponents; solving equations that are literal, linear, quadratic, and proportions; solving systems of two linear equations; operations on complex numbers; evaluating functions; graphs of linear, quadratic, and sinusoidal equations; trigonometry of right and oblique triangles; vectors; and applications of these topics. MTH 152 is required in various technology programs. This course does not fulfill a mathematics requirement for an Associate in Arts or Associate in Science degree.

Prerequisite(s): Any of the following with a grade of C or higher: MTH 096, MTH 098, MTH 099, MTH 104, or MTH 150; or MCC Level 6 Mathematics placement.

Course Learning Outcomes
1. Perform arithmetic calculations with approximate numbers.
2. Perform reductions or conversions to appropriate units of measurement in the measurement systems.
3. Calculate measures of geometric figures which may include perimeter, area, or volume.
4. Perform arithmetic operations on expressions that may include exponents or scientific notation.
5. Use algebraic methods to solve a variety of equations which may include literal, linear, or quadratic.
6. Solve systems of two linear equations in two variables algebraically.
7. Perform arithmetic operations on complex numbers in rectangular form.
8. Evaluate a function expressed in function notation for a specified input value.
9. Find the domain or range of functions.
10. Graph various equations which may include linear, quadratic, or sinusoidal, or functions defined by a table of data.
11. Convert an angle measurement between radians and degrees.
12. Solve applications involving right triangles or oblique triangles.
13. Solve application problems involving the addition of vectors.
14. Determine the features of sinusoidal functions which may include amplitude, period, frequency, or displacement.

A course essential in developing the mathematical competency of the teacher or prospective teacher at the elementary level. Students will develop a comprehensive understanding of the mathematical curriculum recommended by the NCTM (National Council of Teachers of Mathematics) Standards, using a problem solving approach. Topics include historical development of numbers and number systems, study of whole numbers, integers, rationals, irrationals, and reals; abstract number systems; and elementary number theory.
NOTE: MTH 155 is not a teaching methods course.

Prerequisite(s): Any of the following with a grade of C or higher: MTH 096, MTH 098, MTH 099, MTH 104, MTH 160 (or higher); or MCC Level 6 (or higher) Mathematics placement.

Course Learning Outcomes
1. Apply a variety of appropriate strategies to solve problems.
2. Create and use a variety of representations of sets to model physical, social and mathematical phenomena.
3. Illustrate the traditional algorithms for Whole Number, Integer, and Rational Number arithmetic using visual representations.
4. Identify and use the properties of Real Numbers.
5. Employ principles of number theory as a problem solving strategy.
6. Demonstrate the use of physical representations to illustrate numerals in decimal and non-decimal based place value systems.
7. Convert numerals between various positional and additive systems.
8. Incorporate estimation techniques to assess reasonableness of solutions.

A continuation of the concepts of MTH 155, which develop the mathematical competency of the teacher or prospective teacher at the elementary level. Students will develop a comprehensive understanding of the mathematical curriculum recommended by the National Council of Teachers of Mathematics (NCTM) Standards using a problem solving approach with appropriate technology. Topics include probability, statistics, measurement, 2 and 3 dimensional geometry, transformational geometry, coordinate geometry, constructions, congruence and similarity. MTH 156 is a special interest course; check for availability.

Prerequisite: MTH 155 with a grade of C or better.

Course Learning Outcomes
1. Compute various descriptive statistics which may include measures of central tendency, measures of spread, or measures of position.
2. Construct, interpret, or analyze the meaning of a variety of graphs.
3. Predict the probability of outcomes of simple or two-stage experiments or events.
4. Analyze geometric shapes which may include classification or distinguishing between attributes of various shapes.
5. Analyze geometric properties or relationships using principles of coordinate geometry.
6. Apply translations (slides), reflections (flips), rotations (turns), or dilations with 2-dimensional figures.
7. Convert within or between Metric and English systems of measurement.
8. Compute or analyze perimeter, area, or volume for a variety of geometric shapes.
9. Apply principles of congruence, similarity, or proportional reasoning to physical or mathematical situations in application problems.
10. Write explanations to problems at an appropriate elementary grade level.

An introduction to descriptive and inferential statistics intended to give an understanding of statistical techniques and applications in a wide variety of disciplines. Topics include measures of central tendency; dispersion and position; correlation and regression; probability and probability distributions, including binomial and normal; the Central Limit Theorem; parameter estimation and hypothesis testing. Students critically analyze data, acknowledge limitations such as perspective and bias, and develop well-reasoned arguments to form conclusions. Statistical software is used. MTH 160 and MTH 162 have similar content. A student cannot receive credit for MTH 160 if they already have credit for MTH 162.

Prerequisite(s):Any of the following with a grade of C or better: MTH 096, MTH 104, MTH 152, MTH 165 (or higher); or MCC Level 7 mathematics placement.

Course Learning Outcomes
1. Determine a variety of descriptive statistics which may include any of the following measures: central tendency, dispersion, or position.
2. Analyze data using descriptive measures.
3. Produce graphs of data which may include any of the following: histograms, boxplots, or scatterplots.
4. Analyze statistical graphs.
5. Calculate quantitative values for various random variables which may include any of the following types: discrete, binomial, or normal.
6. Interpret probabilities for various probability distributions which may include any of the following types: discrete, binomial, or normal.
7. Use the Central Limit Theorem for applications involving the sampling distribution of the sample mean.
8. Determine confidence intervals for the population mean or the population proportion.
9. Analyze confidence intervals for the population mean or the population proportion.
10. Perform hypothesis tests for the population mean or the population proportion.
11. Determine the linear correlation coefficient for bivariate data.
12. Determine the equation of the least-squares line for bivariate data.
13. Analyze bivariate data.
14. Interpret statistical output.

Statistical inference with an introduction to experimental design. Topics include hypothesis testing and estimation for means, proportions and variances; sample size determination; uses of Chi-square distribution; analysis of variance; linear correlation and regression, non-parametric statistics and statistical research. Students critically analyze data, acknowledge limitations such as perspective and bias, and develop well-reasoned arguments to form conclusions. Statistical software is used.

Prerequisite: MTH 160 with a grade of C or better.

Course Learning Outcomes
1. Estimate statistical parameters in one variable.
2. Estimate statistical parameters in two variables.
3. Perform hypothesis tests of statistical parameters in one variable.
4. Perform hypothesis tests of statistical parameters in two variables.
5. Calculate Type II errors for specified inference problems.
6. Assess Type II errors for specified inference problems.
7. Calculate sample size for specified inference problems.
8. Perform chi-square tests for various applications.
9. Apply Analysis of Variance techniques for one factor applications.
10. Apply Analysis of Variance techniques for two factor applications.
11. Estimate statistical parameters involving linear correlation and linear regression analysis.
12. Perform hypothesis tests of statistical parameters involving linear correlation and linear regression analysis.
13. Differentiate between parametric and nonparametric methods.
14. Choose the appropriate statistical analysis for a given situation.
15. Perform nonparametric tests for various applications.
16. Conduct a statistical study.
17. Assess the validity of a statistical study.
18. Use software to perform various statistical procedures.

An introduction to descriptive and inferential statistics intended to give an understanding of statistical techniques and applications used in the social sciences. Topics include: measures of central tendency, dispersion and position; correlation and regression; probability and probability distributions, including binomial and normal; parameter estimation and hypothesis testing; two-sample analysis; chi-square test of independence; one-way analysis of variance. Students critically analyze data, acknowledge limitations such as perspective and bias, and develop well-reasoned arguments to form conclusions. Statistical software will be used. This course is intended for, but not limited to Social Science majors. Students who have completed MTH 160 or MTH 161 may not receive additional credit for this course.

Prerequisite(s): Prerequisite(s): Any of the following with a grade of C or better: MTH 096, MTH 104, MTH 152, MTH 165 (or higher); or MCC Level 7 mathematics placement.

Course Learning Outcomes
1. Interpret data graphically using measures of central tendency, dispersion, and position
2. Interpret data numerically using measures of central tendency, dispersion, and position
3. Generate a scatter diagram to represent bivariate data
4. Analyze the relationship between variables using linear correlation and linear regression
5. Perform significance tests for linear correlation
6. Classify a random variable as binomial
7. Use the binomial probability distribution to compute probabilities, means, and standard deviations
8. Explain the properties of the normal probability distribution and its parameters
9. Compute probabilities for normal variables as areas, probabilities, or proportions
10. Use the Central Limit Theorem to describe the sampling distribution of the sample mean
11. Produce confidence intervals using both the z and t probability distributions
12. Interpret confidence intervals using both the z and t probability distributions
13. Generate hypothesis tests about mu and p, using both the z and t probability distributions
14. Deduce conclusions about mu and p, using both the z and t probability distributions
15. Perform a two-sample analysis using independent and dependent samples
16. Interpret the results of two-sample analyses using independent and dependent samples
17. Calculate effect size for different samples
18. Interpret the results of effect size for different samples
19. Complete chi-square tests of independence
20. Interpret the results of a chi-square test for independence
21. Execute a one-way analysis of variance
22. Interpret the results of a one-way ANOVA as the effect of a factor on the response variable
23. Use statistical software to produce statistical graphs
24. Use statistical software to compute statistical measures
25. Use statistical software to create estimates of statistical measures
26. Test hypotheses using statistical software to generate necessary values
27. Interpret results obtained using statistical software

A continuation of Statistics I, this course expands upon Statistics I topics to further students’ education surrounding statistical techniques and applications used in the social sciences. Topics include: significance tests for correlation; parameter estimation and hypothesis testing in two-sample analyses; chi-square test of independence; one-way analysis of variance. Students critically analyze data, acknowledge limitations such as perspective and bias, and develop well-reasoned arguments to form conclusions. Statistical software will be used. This course is intended for but not limited to Social Science majors who have already take MTH 160. Students who have completed MTH 161 or MTH 162 may not receive additional credit for this course.

Prerequisite(s): MTH 160 with a grade of C or better

Course Learning Outcomes
1. Perform significance tests for linear correlation.
2. Perform a two-sample analysis using independent and dependent samples.
3. Interpret the results of two-sample analyses using independent and dependent samples.
4. Calculate effect size for different samples.
5. Interpret the results of effect size for different samples.
6. Complete chi-square tests of independence.
7. Interpret the results of a chi-square test for independence.
8. Execute a one-way analysis of variance.
9. Interpret the results of a one-way ANOVA as the effect of a factor on the response variable.
10. Use statistical software to create estimates of statistical measures.
11. Test hypotheses using statistical software to generate necessary values.

A first course in trigonometry. Topics include the trigonometric ratios, radian measure, angles in a coordinate system, ratio values for any angle, graphs of trigonometric functions and basic trigonometric identities and equations. A specific calculator may be required of students in this course. Students are advised to check with their instructor.

Prerequisite: MTH 104 with a grade of C or better, or MCC Level 8 Mathematics Placement.

Course Learning Outcomes
1. Draw an angle in standard position on coordinate axes when given the angle measure in radians.
2. Define (in terms of x, y, and r) any of the six trigonometric ratios for an angle in standard position whose terminal side passes through the point (x, y) on a circle of radius r.
3. Find the exact values of any of the six trigonometric ratios for quadrantal angles or special angles.
4. Solve first-degree trigonometric equations for exact values of the variable or for approximate values of the variable.
5. Establish new trigonometric identities by applying algebraic techniques and identities such as reciprocal, quotient or Pythagorean.
6. Analyze characteristics of trigonometric functions.
7. Perform angle measurement conversions, such as decimal degrees; degrees, minutes, seconds; or radians.

This course is intended to enhance algebraic skills and graphing techniques, and to prepare students for Precalculus Mathematics and Applied Calculus. Topics include functions that are quadratic, polynomial, piecewise, exponential and logarithmic; equations that are quadratic in form, involve radicals, absolute value, variation and rational exponents; inequalities that are polynomial, rational, and absolute value.

Prerequisite: MTH 104 with a grade of C or better, or MTH 140 with a grade of C or better, or MCC Level 8 Mathematics placement.

Course Learning Outcomes
1. Solve a variety of equations which may include any of the following types: quadratic in form, radical, rational exponent, linear absolute value, exponential, or logarithmic.
2. Solve a variety of inequalities which may include any of the following types: linear absolute value, factorable polynomial, or rational.
3. Graph a variety of relations which may include any of the following types: polynomial of degree at most 4, absolute value, square root, cube root, reciprocal, exponential, logarithmic, piecewise, or circle.
4. Describe or graph transformations of functions which may involve any combination of a horizontal shift, a vertical shift, or a reflection.
5. Convert between any of the three forms: a graph, an equation, or a verbal description of attributes such as zeros, intercepts, or domain.
6. Determine a composition or combination of functions.
7. Determine the inverse of a one-to-one function.
8. Determine the zeros of a polynomial function using synthetic division with related theorems.
9. Use long division to divide polynomials.
10. Rewrite a logarithmic expression using properties of logarithms.
11. Solve a variety of applications using variation, exponential, or logarithmic models.

An introduction to discrete mathematics primarily intended for students majoring in Information Technology or Computer Systems Technology. The emphasis will be on the development of technical discrete mathematics skills, rather than rigorous proof. Topics will include number systems, sets, logic, induction, elementary counting techniques, relations, functions, matrices, and Boolean algebra.

Note: This course is not designed for students intending to major in Mathematics or Computer Science. Students intending to major in Mathematics or Computer Science should take MTH 220.

Prerequisite: MTH 141 or MTH 165 with a grade of C or better, or MCC Level 9 Mathematics placement, or equivalent.

Course Learning Outcomes
1. Convert between different number systems
2. Apply standard set operations.
3. Assess the validity of an argument with truth tables or rules of inference.
4. Evaluate finite sums given in sigma notation.
5. Solve counting problems with permutations or combinations.
6. Conclude whether a given relation is an equivalence relation.
7. Classify a given function as one-to-one or onto.
8. Compare the growth rates of functions with Big-O notation.
9. Apply standard matrix operations.
10. Apply the axioms of a Boolean algebra.

A study of the properties and graphs of functions, including polynomial, absolute value, power, piecewise, radical, rational, exponential, logarithmic, trigonometric, and inverse trigonometric. Topics also include a study of analytic trigonometry and an introduction to vectors. This course is intended to prepare students for the study of calculus.

Prerequisite: MTH 165 with a grade of C or higher, or MTH 141 with a grade of C or higher, or MCC Level 9 Mathematics placement or higher.

Course Learning Outcomes
1. Rewrite a logarithmic expression using properties of logarithms.
2. Perform operations on functions, which may include compositions or arithmetic combinations.
3. Determine simplified difference quotients.
4. Determine the inverse of a one-to-one function.
5. Construct graphs of equations, functions, or their transformations.
6. Identify appropriate features of the graph of an equation such as intercepts, asymptotes, maximum values, minimum values, domain, range, or symmetry.
7. Determine the values (in exact form when possible) of the trigonometric functions of any angle.
8. Verify a trigonometric identity.
9. Solve a trigonometric equation.
10. Evaluate expressions involving inverse trigonometric functions.
11. Use the Law of Sines and/or Law of Cosines to solve an oblique triangle.
12. Construct the graph of y = a f (bx + c) + d where f is a trigonometric function.
13. Identify appropriate features of the graph of a trigonometric function, such as amplitude, period, phase shift, vertical shift, domain, or range.
14. Perform operations on vectors.

An intuitive introduction to the principal ideas of differential and integral calculus. Among the topics covered are: functions (including exponential and logarithmic), limits, differentiation, and integration. Emphasis will be placed upon the use of calculus in solving problems from areas including business, economics, and the social and natural sciences.

Prerequisite: MTH 165 with grade of C or better, or MCC Level 9 Mathematics placement, or equivalent.

Course Learning Outcomes
1. Evaluate limits using analytical methods.
2. Evaluate limits using numerical methods.
3. Evaluate limits graphically.
4. Apply the definition of continuity at a point to determine continuity.
5. Examine the relationship between the limit definition of a derivative and the average rate of change of a function.
6. Apply the rules of differentiation to obtain derivatives of functions.
7. Sketch a function by interpreting the derivatives of the function.
8. Find the local or relative extreme values of a function by interpreting the derivatives of a function.
9. Evaluate antiderivatives using analytical methods.
10. Evaluate definite integrals.
11. Examine the relationship between the area under a curve and the definite integral.
12. Evaluate partial derivatives of functions of several variables.
13. Evaluate second order partial derivatives of functions of several variables.
14. Solve application problems by applying calculus techniques.

A first course in single variable calculus. Topics include limits and continuity; differentiation of algebraic, trigonometric, exponential, logarithmic, and inverse trigonometric functions; applications of derivatives to curve sketching, related rates, optimization, and rectilinear motion; indefinite and definite integrals; both parts of the Fundamental Theorem of Calculus; applications of definite integrals to area, average value, and rectilinear motion; and integration by u-substitution. A specific calculator may be required of students in this course. Students are advised to check with the instructor.

Prerequisite: MTH 175 with grade of C or higher, or high school precalculus course taken within the last three years with a grade of B (83) or higher, or MCC Level 10 Mathematics placement.

Course Learning Outcomes
1. Determine a variety of limits which may include any of the following types: one-sided limits, two-sided limits, infinite limits, or limits at infinity.
2. Determine whether a function is continuous at a given point.
3. Differentiate a variety of functions using the limit definition of the derivative.
4. Determine whether a function is differentiable at a given point.
5. Differentiate combinations or compositions of a variety of functions which may include any of the following: polynomial, radical, rational, trigonometric, inverse trigonometric, exponential, or logarithmic.
6. Differentiate implicitly defined functions.
7. Use derivatives to determine key features of graphs of functions which may include any of the following: intervals of increase or decrease, intervals of concavity, extrema, or points of inflection.
8. Determine indefinite integrals.
9. Approximate definite integrals with Riemann Sums.
10. Apply the Fundamental Theorem of Calculus.
11. Use the method of integration by u-substitution.
12. Use methods of Calculus to solve a variety of applications which may include any of the following types: related rates, optimization, rectilinear motion, area, or average value.

A second course in single variable calculus. Topics include techniques of integration, applications of definite integrals, first order separable differential equations, indeterminate limit forms, improper integrals, infinite series, Taylor polynomials, and power series. A specific calculator may be required of students in this course.

Prerequisite: MTH 210 with a grade of C or higher.

Course Learning Outcomes
1. Compute indefinite integrals using a variety of techniques which could include: substitution, integration by parts, trigonometric substitution, or partial fraction decomposition.
2. Formulate a definite integral to solve a variety of applications.
3. Evaluate a definite integral using the Fundamental Theorem of Calculus.
4. Estimate the value of a definite integral using one or more of the following techniques: the Midpoint Rule, the Trapezoid Rule, and Simpson’s Rule.
5. Estimate the value of a definite integral using a Taylor Polynomial.
6. Use L’Hopital’s Rule to evaluate a limit.
7. Evaluate an improper integral using the appropriate limit definition.
8. Translate verbal descriptions involving rates of change into differential equations.
9. Solve a separable differential equation using separation of variables.
10. Justify whether a given series converges or diverges.
11. Determine the interval and radius of convergence for a given power series.

A course in multivariable calculus. Topics include three-dimensional space, vectors, parametric equations, polar coordinates, derivatives and integrals of vector-valued functions, functions of several variables, partial derivatives, multiple integrals, vector fields, and line integrals. A specific calculator may be required of students in this course. Students are advised to check with the instructor.

Prerequisite: MTH 211 with a grade of C or higher.

Course Learning Outcomes
1. Perform vector operations.
2. Analyze functions of several variables represented numerically, graphically, or algebraically using the methods of calculus.
3. Apply the gradient to produce the directional derivative of a function of several variables.
4. Apply the gradient to produce the direction and magnitude of the maximum increase of the function at a given point.
5. Determine the critical points of a function of two variables.
6. Classify critical points as relative minima, relative maxima, saddle points, or none of these.
7. Compute multiple integrals.
8. Represent curves parametrically, implicitly, or explicitly.
9. Classify a given vector field as conservative or nonconservative.
10. Evaluate a line integral through a given vector field.

A course in Discrete Mathematics with an emphasis on the development of formal mathematical proof writing skills. Methods of proof covered include direct proof, proof by contraposition, proof by contradiction, division into cases, and mathematical induction. Students will be expected to create coherent structured arguments using sound logical reasoning and mathematically correct terminology and notation. Topics include propositional and predicate logic, elementary number theory, set theory, functions, relations, and combinatorics.

Prerequisite: MTH 210 with a grade of C or higher, or equivalent.

Course Learning Outcomes
1. Use and interpret mathematically correct terminology and notation.
2. Apply logical reasoning to solve a variety of problems.
3. Formulate a correct proof of a universally quantified statement.
4. Propose a counter example to demonstrate that a statement is false.
5. Solve a variety of combinatorial problems.
6. Classify a function using concepts such as one-to-one, onto, and bijection.
7. Analyze a given relation to determine whether or not it is reflexive, symmetric, transitive, or an equivalence relation.

An introduction to ordinary differential equations and their applications. Analytical methods include: separation of variables, linear first order equations, substitution methods, second order linear equations with constant coefficients, undetermined coefficients, variation of parameters, autonomous systems of two first order equations, series solutions about ordinary points, and the Laplace Transform. In addition to analytical methods, quantitative and qualitative analysis will be employed through the use of Euler’s Method, phase lines, phase planes, and slope fields.

Prerequisite: MTH 211 with a grade of C or better.

Course Learning Outcomes
1. Classify a differential equation using appropriate mathematical terminology.
2. Solve a variety of differential equations using analytical methods.
3. Describe the qualitative behavior of the solutions of a differential equation.
4. Estimate the solutions of a differential equation using numerical and graphical methods.
5. Solve a differential equation using power series.
6. Solve an autonomous system of two first order differential equations.
7. Examine the qualitative behavior of the solutions of an autonomous system of two first order differential equations.
8. Solve initial value problems using the Laplace Transform.
9. Solve applied problems using differential equations.

Topics include systems of linear equations, vectors and matrices, determinants, vector spaces, linear transformations, eigenvectors and eigenvalues, and inner product spaces. Course also offered in Summer.

Prerequisite: MTH 212 with a grade of C or better, or both MTH 211 and MTH 220 with a grade of C or better in each, or permission of instructor.

Course Learning Outcomes
1. Apply standard matrix operations.
2. Formulate the inverse of a square matrix or determine that the inverse does not exist.
3. Identify conditions that are equivalent to a square matrix being invertible.
4. Evaluate determinants of square matrices using cofactor expansion or row reduction.
5. Solve systems of linear equations by a variety of methods which may include any of the following: Gaussian elimination, Gauss-Jordan elimination, using an inverse matrix (if applicable), or Cramer’s rule (if applicable).
6. Prove that a given subset of a vector space is a subspace or demonstrate that it is not.
7. Prove that a given function is a linear transformation or demonstrate that it is not.
8. Classify sets of vectors using terms such as linearly independent, linearly dependent, basis, orthogonal, or orthonormal
9. Calculate the eigenvalues of a square matrix.
10. Construct bases for a variety of subspaces, which may include any of the following: row space of a matrix, column space of a matrix, null space of a matrix, eigenspace of a matrix, kernel of a linear transformation, or range of a linear transformation.
11. Construct an orthonormal basis for an inner product space by using the Gram-Schmidt process.
12. Diagonalize a square matrix or determine that it is not diagonalizable.

A calculus-based course in probability and statistics. Topics include probability axioms, discrete and continuous random variables and their probability distributions, multivariate probability distributions, functions of random variables, and the Central Limit Theorem. A statistical software package such as Minitab or R will be used.

MTH 212 with a grade of C or higher OR MTH 211 AND MTH 220 each with a grade of C or higher.

Course Learning Outcomes
1. Apply probability results to solve application problems of different disciplines.
2. Classify random variables using appropriate mathematical terminology.
3. Determine the probability distributions of random variables.
4. Determine multivariate probability distributions.
5. Compute the parameters of random variables.
6. Use the parameters of random variables to solve probability problems.
7. Apply Chebyshev’s Theorem to provide meaningful bounds for probabilities of interest.
8. Calculate event probabilities by hand using calculus.
9. Calculate event probabilities using appropriate theorems.
10. Select the correct probability model for a given problem.
11. Apply theorems concerning the distributions of functions of random variables to probability problems.
12. Prove basic probability results.

See the Department Chairperson.

Check if course is offered:
Fall Semester 2025
Intersession 2026
Spring Semester 2026