2023-2024 Schoolcraft Catalog [ARCHIVED CATALOG]
Mathematics
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Students interested in mathematics will find the array of courses available at Schoolcraft covering basic math, intermediate algebra, trigonometry, statistics, pre-calculus, calculus, calculus with analytic geometry, linear algebra, and differential equations. Students can also expand their mathematics educational opportunities through a variety of student activities, clubs, and organizations:
- Join the Math and Physics Club, which offers challenging activities and an annual competition.
- Compete for the Pythagorean Prize, which honors two top winners each year with cash prizes and recognition.
- Publish student-authored articles and research in The Right Angle.
There is currently no certificate or degree program offered in Mathematics. Some or all of the courses listed below may be required/recommended or applied toward a certificate or degree program in another area of study. These courses may also be taken for personal or professional interest or for transfer to a four-year college or university.
Students interested in studying Mathematics should talk to their Academic Advisor about transfer guides and articulation agreements with Schoolcraft College. Students interested in studying Mathematics at a 4-year university may be interested in completing the Associate of Arts, Associate of Engineering, or the Associate of Science degree at Schoolcraft College.
Degrees
Transfer Degrees
Mathematics
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MATH 011 - Applications - Utility of Math Support
Credits: 2
Lecture Contact Hours: 1
Lab Contact Hours: 1
Description: This course is designed to provide students with supplemental support and instruction to promote success in MATH 111 . These topics include, but are not limited to: solving equations and inequalities, appropriate use and manipulation of formulas, analysis of mathematical verbiage, and using critical reading and writing to assess the correctness of solutions. Study skills such as time management, productive homework habits, note-taking, and problem-solving will also be covered.
Prerequisites: A minimum score of 11 ACT-Math, 15 SAT-Math, 23 CPT-Arithmetic, or 220 NGA-Arithmetic. Or Overall High School GPA of 2.7-1.8.
Corequisites: MATH 111 .
Recommended: None
Course Category: Liberal Arts | Mathematics
This Course is Typically Offered: Winter and Fall
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Course Competencies
- Calculate sums, differences, products, and quotients of fractions.
- Solve linear equations and inequalities.
- Solve percentage problems.
- Solve proportion problems.
- Determine when to use appropriate formulas, including the Pythagorean Theorem and trigonometric formulas.
- Verify solutions to equations and inequalities.
- Convert between fractions, decimals, and percents.
- Explore time/goal management techniques to support college success.
- Devise a plan for successfully completing MATH 111.
- Interpret logic-based terminology correctly, such as “and” versus “or” and “at least.”
- Round numeric quantities accurately and appropriately.
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MATH 013 - Intermediate Algebra Support
Credits: 2
Lecture Contact Hours: 1
Lab Contact Hours: 1
Description: This course is designed to provide students with supplemental support and instruction to promote success in MATH 113 . These topics include but are not limited to, fundamental operations with real numbers and polynomials, graphing, linear equations, factoring polynomials, rational expressions, exponents, and quadratic equations. Study skills such as time management, productive homework habits, note-taking, and problem-solving will also be covered.
Prerequisites: A minimum score of 16 ACT-Math, 22 SAT-Math, 75 CPT-Elementary Algebra, 230 NGA-Quantitative Reasoning, Algebra, and Statistics or overall High School GPA of 1.8 - 2.7 or higher.
Corequisites: MATH 113
Recommended: None.
Course Category: Liberal Arts | Mathematics
This Course is Typically Offered: Fall, Winter
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Course Competencies
- Transform composite numbers and polynomials into factored form.
- Calculate operations with rational expressions and equations.
- Apply order of operations to simplify expressions.
- Solve linear equations and inequalities.
- Transform inequalities into interval notation.
- Apply graphing techniques to points and lines.
- Break down application problems into mathematical models.
- Demonstrate exponent rules.
- Calculate operations with radical expressions and equations.
- Explore time/goal management techniques to support college success.
- Devise a plan for successfully completing MATH 113.
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MATH 022 - Elementary Statistics Support
Credits: 3
Lecture Contact Hours: 1.5
Lab Contact Hours: 1.5
Description: This course serves as a supplement to MATH 122 - Elementary Statistics. MATH 022 involves the review of basic arithmetic and algebraic techniques that are necessary for success in MATH 122 . Additionally, the development of study skills, as well as the utilization of College resources, will be stressed throughout the course. Problem-solving skills and critical thinking skills will be developed throughout the course.
Prerequisites: MATH 047 with a minimum grade of 2.0 or 16 ACT, 22 SAT, 75 CPT-AR, 28 CPT-EA, 260 NGA-AR, 230 NGA-QRAS or Overall high school GPA of 2.7-1.8.
Corequisites: MATH 122
Recommended: None
Course Category: Liberal Arts | Mathematics
This Course is Typically Offered: Winter and Fall
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Course Competencies
- Explore relationships of proportions.
- Develop strategies for application problems.
- Investigate the relationship between fractions, decimals and the percent form of numbers.
- Analyze graphical displays.
- Apply mathematical terminology.
- Examine techniques used in simplifying algebraic and numerical expressions.
- Examine techniques used in solving algebraic equations.
- Explore graphs of equations in two variables.
- Explore the make-up of a data set.
- Investigate simple and compound linear inequalities in one variable.
- Explore linear equations and inequalities in two variables.
- Develop study skills.
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MATH 045 - Basic Mathematics
Credits: 4
Lecture Contact Hours: 4
Description: The topics covered in this course include arithmetic with whole numbers, fractions, decimals, percentages and proportions. In addition, several topics from geometry are included.
Prerequisites: Minimum score of 11 ACT-Math, 15 SAT-Math, 23 CPT-Arithmetic or 220 NGA-Arithmetic. Competence with addition, subtraction, multiplication and division of whole numbers without the aid of a calculator.
Corequisites: None.
Recommended: None.
Course Category: Applied Liberal Arts | Mathematics
This Course is Typically Offered: Winter, Spring, Summer, Fall
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Course Competencies
- Calculate sums, differences, products and quotients involving fractions.
- Solve ax = b and x + a = b where a and b are whole numbers, fractions or decimals.
- Convert between fraction, decimal and percent forms of a number.
- Compare quantities using ratios or unit rates.
- Solve consumer applications.
- Calculate sums, differences, products and quotients involving decimals.
- Solve proportion problems.
- Solve percentage problems.
- Apply the order of operations procedure.
- Apply mathematical terminology, such as sum, product, difference, quotient, commutative, associative, factor, multiple, prime, etc.
- Calculate perimeters of polygons and circumference of a circle.
- Calculate areas of rectangles, triangles and circles.
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MATH 047 - Prealgebra
Credits: 3
Lecture Contact Hours: 3
Description: Topics covered in this course include an introduction to variables, integers and algebraic expressions; simplifying algebraic expressions involving integers, fractions and decimals; solving algebraic equations involving integers, fractions, decimals and percents; ratio and proportions; applications using basic concepts from geometry; and introduction to graphing via point-plotting.
Prerequisites: MATH 045 with a minimum grade of 2.0 or a minimum score of 16 ACT-Math, 22 SAT-Math, 60 CPT-Arithmetic, 240 NGA-Arithmetic or 220 NGA-Quantitative Reasoning, Algebra and Statistics. Competence in arithmetic without the aid of a calculator.
Corequisites: None.
Recommended: None.
Course Category: Applied Liberal Arts | Mathematics
This Course is Typically Offered: Winter, Spring, Summer, Fall
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Course Competencies
- Calculate sums, differences, products and quotients involving integers.
- Apply order of operations to mathematical problems.
- Solve linear equations involving integers, fractions and decimals.
- Solve percentage problems.
- Solve proportion problems.
- Solve problems involving perimeter, area, volume and the Pythagorean theorem.
- Translate English expressions into mathematical expressions.
- Graph linear equations by plotting points.
- Simplify expressions using properties of exponents.
- Simplify fractional expressions.
- Evaluate algebraic expressions.
- Factor the greatest common factor (GCF) from a polynomial expression.
- Apply the prime factorization method to greatest common factor (GCF) or least common multiple (LCM) problems.
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MATH 053 - Beginning Algebra
Credits: 4
Lecture Contact Hours: 4
Description: This course will explore the real number system, fundamental operations with real numbers, graphing, linear equations, factoring polynomials, rational expressions, exponents, quadratic equations, applications and introduction to the function concept.
Prerequisites: MATH 047 with a minimum grade of 2.0 or a minimum score of 16 ACT-Math, 22 SAT-Math, 75-CPT-Arithmetic, 28 CPT-Elementary Algebra, 260 NGA-Arithmetic or 230 NGA-Quantitative Reasoning, Algebra and Statistics.
Corequisites: None.
Recommended: None.
Course Category: Applied Liberal Arts | Mathematics
This Course is Typically Offered: Winter, Spring, Summer, Fall
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Course Competencies
- Apply properties of arithmetic and algebra to simplify and evaluate algebraic expressions.
- Express the sums, differences, products and quotients of polynomials in simplest form.
- Express the sums, differences, products and quotients of rational expressions in simplest form.
- Solve linear equations in one variable.
- Solve linear inequalities in one variable.
- Factor polynomials.
- Solve quadratic equations by factoring.
- Solve rational equations.
- Solve literal equations for a specified variable.
- Solve applications using linear equations in one variable, quadratic equations or rational equations.
- Graph linear equations in two variables using a table of values, x and y intercepts or slope/y-intercept.
- Write a linear equation in two variables using slope-intercept form, point-slope form or standard form.
- Explore the function concept using the vertical line test, determining the domain and range from a graph or by evaluating functions.
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MATH 101 - Business Mathematics
Credits: 3
Lecture Contact Hours: 3
Description: This course offers a review of fundamentals of arithmetic along with coverage of percentage, simple and compound interest, taxes, insurance, bonds and their applications to business practice.
Prerequisites: MATH 045 with a minimum grade of 2.0, or overall high school GPA of 2.8 or higher, a minimum score of 16 ACT-Math, 22 SAT-Math, 60 CPT-Arithmetic, or 240 NGA-Arithmetic
Corequisites: None.
Recommended: None.
Course Category: Liberal Arts | Mathematics
This course counts toward Schoolcraft’s General Education Requirements.
This Course is Typically Offered: Winter, Spring, Summer, Fall
Check Course Availability
Course Competencies
- Calculate basic arithmetic problems with whole numbers, fractions, decimals, percents and ratios.
- Solve algebraic equations and word problems.
- Use key terminology related to business mathematics.
- Balance a checking account.
- Compute gross pay, employee deductions and employer contributions.
- Solve problems involving simple and compound interest, promissory notes and present value.
- Calculate maturity dates, values and time periods related to loans.
- Calculate various types of discounts on invoices.
- Compute markup and markdown on items.
- Calculate present or future value of an annuity.
- Calculate amount of a sinking fund and amortization payment.
- Calculate payments and costs associated with both open- and closed- end credit.
- Determine the most cost effective mortgage based on the payment details and costs.
- Calculate depreciation using standard methods.
- Solve problems involving life, property and motor vehicle insurances.
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MATH 102 - Technical Mathematics
Credits: 4
Lecture Contact Hours: 4
Description: Technical Mathematics provides the practical mathematics skills needed in a wide variety of occupational programs. Students in this course will address topics including measurement, basic algebra, geometry, right triangle trigonometry, graphing and statistics.
Prerequisites: MATH 047 with a minimum grade of 2.0, or overall high school GPA of 2.8 or higher, a minimum score of 16 ACT-Math, 22 SAT-Math, 75 CPT-Arithmetic, 28 CPT-Elementary Algebra, 260 NGA-Arithmetic or 230 NGA-Quantitative Reasoning, Algebra and Statistics
Corequisites: None.
Recommended: None.
Course Category: Liberal Arts | Mathematics
This course counts toward Schoolcraft’s General Education Requirements.
This Course is Typically Offered: Fall, Winter
Check Course Availability
Course Competencies
- Utilize knowledge of ratios, percentages and proportions to solve technical application problems.
- Determine measurements using technical tools.
- Apply conversion equations to technical problems.
- Calculate conversions between mixed numbers, fractions, decimals and percents.
- Analyze measurement parameters such as accuracy, precision and tolerance.
- Develop equations and inequalities to represent problems of a technical nature.
- Solve equations of a technical nature with one or two variables.
- Solve linear inequalities.
- Calculate angles, perimeter, area and volume with geometric formulas.
- Solve problems using trigonometric ratios and the Pythagorean Theorem.
- Analyze the construction and interpretation of graphs.
- Calculate measures of central tendency of data.
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MATH 105 - Mathematics for Elementary Teachers 1
Credits: 4
Lecture Contact Hours: 4
Description: This is the first of a two-course sequence designed for students who plan to enter elementary school teaching. The course examines elementary school math topics and mathematics curriculum from an advanced standpoint with an emphasis on conceptual understanding and problem solving. The course covers problem solving, number theory, sets, algebraic concepts and functions, numeration, the real numbers and their properties and operations.
Prerequisites: MATH 053 with a minimum grade of 2.5, or overall high school GPA of 2.8 or higher, a minimum score of 19 ACT-Math, 25 SAT-Math, 100 CPT-Elementary Algebra, 270 NGA-Arithmetic or 250 NGA-Quantitative Reasoning, Algebra and Statistics
Corequisites: None.
Recommended: None.
Course Category: Liberal Arts | Mathematics
This course counts toward Schoolcraft’s General Education Requirements.
This Course is Typically Offered: Fall, Winter
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Course Competencies
- Apply Polya’s four-step plan in analyzing and solving problems.
- Demonstrate clear presentation of problem solving strategies to include the use of tables, charts, Venn diagrams and algebra.
- Compare inductive and deductive reasoning as related to logic, the foundation of the mathematics.
- Investigate special number patterns and sequences (to include arithmetic and geometric) and relate these number patterns to the study of functions.
- Apply concepts from elementary Number Theory, to include primes, composites, divisibility tests, greatest common factor and least common multiple.
- Apply concepts from set theory and set operations as the language and symbols of the mathematics.
- Investigate place value, base ten materials and other models for numeration systems.
- Model arithmetic operations using set or measurement models.
- Apply properties of real numbers.
- Explain arithmetic operations with a variety of paper and pencil algorithms to include mental math strategies (without the use of a calculator).
- Construct models for representing, operating with and solving problems involving fractions and decimals.
- Construct models for representing, operating with and solving problems involving percents and proportions.
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MATH 106 - Mathematics for Elementary Teachers 2
Credits: 4
Lecture Contact Hours: 4
Description: This is the second of a two-course sequence designed for students who plan to enter elementary school teaching. The course examines elementary school math topics and mathematics curriculum from an advanced standpoint with an emphasis on conceptual understanding and problem solving. The course covers geometry, measurement, statistics and probability.
Prerequisites: MATH 105 with a minimum grade of 2.0.
Corequisites: None.
Recommended: None.
Course Category: Liberal Arts | Mathematics
This course counts toward Schoolcraft’s General Education Requirements.
This Course is Typically Offered: Fall, Winter
Check Course Availability
Course Competencies
- Solve problems in two- and three-dimensional geometry using multiple strategies, including technological approaches.
- Explain concepts about two- and three-dimensional geometry.
- Solve problems involving measurement and the metric system.
- Explain concepts of measurement and the metric system.
- Solve problems involving length and area.
- Solve problems involving surface area and volume.
- Construct graphs to organize and display data by hand and using technological tools.
- Analyze data using simple statistical methods and technological tools.
- Interpret data and statistical information graphically.
- Apply principles of elementary probability and inference applicable to game and real-world situations.
- Explain methods of probability and inference applicable to game and real-world situations.
- Solve problems involving expected value, odds and conditional probability.
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MATH 111 - Applications - Utility of Math
Credits: 4
Lecture Contact Hours: 4
Description: This course is intended for students who do not wish to pursue the study of mathematics by following the standard sequence of courses, but who need to develop some competency in mathematics for an Associate of Arts degree. This course includes the practical application of mathematics. Topics covered in the course include geometry, managing money, interest, installment buying, credit cards, loans, probability, statistics and graphing.
Prerequisites: MATH 047 with a minimum grade of 2.0, or overall high school GPA of 2.8 or higher, a minimum score of 16 ACT-Math, 22 SAT-Math, 75 CPT-Arithmetic, 28 CPT-Elementary Algebra, 260 NGA-Arithmetic or 230 NGA-Quantitative Reasoning, Algebra and Statistics.
Corequisites: None.
Recommended: None.
Course Category: Liberal Arts | Mathematics
This course counts toward Schoolcraft’s General Education Requirements.
This course counts toward a Michigan Transfer Agreement General Education Requirement.
This Course is Typically Offered: Winter, Spring, Summer, Fall
Check Course Availability
Course Competencies
- Solve problems involving simple or compound interest.
- Solve consumer problems involving installment buying, credit cards or mortgages.
- Use annuity formulas in problems involving retirement planning or college savings.
- Use combinations or permutations to count the number of ways an event could occur.
- Solve problems using basic principles of probability.
- Use frequency distributions or histograms to display data sets.
- Analyze a data set using measures of central tendency and variation.
- Draw conclusions about a normal distribution.
- Solve systems of linear equations graphically or algebraically.
- Solve optimization problems using linear programming.
- Calculate perimeter, area and volume of geometric shapes and solids.
- Solve problems involving similar triangles, the Pythagorean Theorem or right triangle trigonometric ratios.
- Graph linear equations in two variables using a table of values, x- and y-intercepts or slope/y-intercept.
- Write linear equations and inequalities in two variables to represent a practical application.
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MATH 113 - Intermediate Algebra for College Students
Credits: 4
Lecture Contact Hours: 4
Description: Review of algebraic operations; problem-solving strategies; integer and rational exponents; complex numbers; solving equations; function concepts; graphs and applications of linear, quadratic, exponential, and logarithmic functions; and systems of equations are the topics covered in this course.
Prerequisites: MATH 053 with a minimum grade of 2.0, or overall high school GPA of 2.8 or higher, or a minimum score of 19 ACT-Math, 25 SAT-Math, 78 CPT-Elementary Algebra or 250 NGA-Quantitative Reasoning, Algebra and Statistics
Corequisites: None.
Recommended: None.
Course Category: Liberal Arts | Mathematics
This course counts toward Schoolcraft’s General Education Requirements.
This Course is Typically Offered: Winter, Spring, Summer, Fall
Check Course Availability
Course Competencies
- Solve linear and quadratic equations and related applications using one variable.
- Solve equations that are quadratic in form and related applications using one variable.
- Solve radical equations and related applications using one variable.
- Solve rational equations and related applications using one variable.
- Solve exponential and logarithmic equations and related applications using one variable.
- Perform operations on functions.
- Transform radical expressions to the simplest form.
- Transform expressions with integer and rational exponents to simplest form.
- Solve linear systems of equations algebraically and graphically.
- Translate application problems into a linear system.
- Solve simple and compound linear inequalities in one variable both algebraically and graphically.
- Solve second-degree inequalities in one variable both algebraically and graphically.
- Solve first-degree inequalities in two variables both algebraically and graphically.
- Solve inequalities and equations containing absolute value both algebraically and graphically.
- Solve applications of functions involving two variables.
- Determine the inverse of a function algebraically or graphically.
- Graph quadratic functions.
- Graph exponential and logarithmic functions.
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MATH 119 - Trigonometry
Credits: 3
Lecture Contact Hours: 3
Description: Trigonometric functions and their graphs, identities, equations and inverse functions and solutions of right and oblique triangles are the topics included in this course.
Prerequisites: MATH 113 with a minimum grade of 2.0 or a minimum score of 23 ACT-Math, 29 SAT-Math, 63 CPT-College-Level Math or 230 NGA-Advanced Algebra and Functions.
Corequisites: None.
Recommended: None.
Course Category: Liberal Arts | Mathematics
This course counts toward Schoolcraft’s General Education Requirements.
This course counts toward a Michigan Transfer Agreement General Education Requirement.
This Course is Typically Offered: Winter, Spring, Summer, Fall
Check Course Availability
Course Competencies
- Evaluate the basic trigonometric functions using degree or radian measure.
- Evaluate the basic trigonometric functions involving angles in standard position.
- Evaluate the basic trigonometric functions involving right triangles.
- Evaluate the basic trigonometric functions involving the unit circle.
- Solve right and oblique triangles.
- Solve trigonometric equations.
- Verify trigonometric identities.
- Graph trigonometric functions.
- Construct mathematical models using trigonometric functions.
- Solve application problems using trigonometry.
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MATH 122 - Elementary Statistics
Credits: 4
Lecture Contact Hours: 4
Description: This course includes an introduction to statistics, statistical descriptions, frequency distributions, possibilities and probabilities, probability distributions, sampling and sampling distributions, testing hypotheses based on measurements, count data, paired data and use of nonparametric tests.
Prerequisites: MATH 113 with a minimum grade of 2.0 or a minimum score of 23 ACT-Math, 29 SAT-Math, 63 CPT-College-Level Math or 265 NGA-Quantitative Reasoning, Algebra and Statistics.
Corequisites: None.
Recommended: None.
Course Category: Liberal Arts | Mathematics
This course counts toward Schoolcraft’s General Education Requirements.
This course counts toward a Michigan Transfer Agreement General Education Requirement.
This Course is Typically Offered: Winter, Spring, Summer, Fall
Check Course Availability
Course Competencies
- Create visual presentations using sample data both by hand and by using statistical software, including a tabular frequency distribution, stem-and-leaf plot, histogram, frequency polygon and pie chart.
- Compute descriptive statistics both by using an algorithm and by using statistical software, including the mean, median, mode, fractiles, range, variance and standard deviation.
- Determine whether a given sampling method yields a random sample, simple random sample, stratified sample, etc.
- Use a random number generator to select a random sample from a given population.
- Determine the number of possible outcomes of an event with the aid of the addition, multiplication, complement, factorial and other rules.
- Calculate probability of an event by using the classical approach.
- Estimate the probability of an event by using the relative frequency approach.
- Determine the conditional probability of one event given another event by using the defining formula for conditional probability.
- Determine probabilities for various discrete distributions (including the uniform, binomial and hypergeometric) by all of the following means: a formula, a table and statistical software.
- Determine probabilities for various continuous distributions (including the Gaussian normal and Student’s t) by using a formula and either a table or statistical software.
- Interpret probabilities of a discrete random variable as the area of bars in its histogram.
- Interpret probabilities of a continuous random variable as the area under the graph of its density function.
- Solve practical problems involving probability distributions.
- Determine the mean (expected) value and the standard deviation of a discrete random variable using its probability distribution.
- Determine whether two events are independent of one another by using their probabilities.
- Determine a confidence interval for a population mean, based on a random sample and the normal or t-distribution (as appropriate), both by using a formula and table and by using statistical software.
- Test a hypothesis regarding one, two or several population means, based on random sample(s) and the normal, t- or ANOVA distribution (as appropriate), both by using a formula and table and by using statistical software.
- Determine a confidence interval for a population proportion, based on a random sample and the normal distribution, both by using a formula and table and by using statistical software.
- Test a hypothesis regarding one, two or several population proportions, based on a random sample(s) and the normal, t or chi-squared distribution (as appropriate), both by using a formula and table and by using statistical software.
- Determine Pearson’s linear correlation coefficient r for a sample of bivariate data, both by using a formula and by using statistical software.
- Determine the least-squares linear regression fit to a sample bivariate data.
- Test a hypothesis regarding the linear correlation between two variables, based on a random sample and on critical values of the r-distribution, both with the aid of a table and the aid of statistical software.
- Test a hypothesis regarding one or two population medians or a population proportion, based on a random sample(s) and the sign test.
- Test a hypothesis regarding the linear correlation between two variables, based on a random sample and Spearman’s rank-correlation test.
- Investigate sampling distributions of statistics.
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MATH 126 - College Algebra
Credits: 4
Lecture Contact Hours: 4
Description: The function concept, polynomial, rational, exponential and logarithmic functions, curve sketching, graphical analysis of functions, graphical solutions and business applications are the topics included in this course.
Prerequisites: MATH 113 with a minimum grade of 2.0 or a minimum score of 23 ACT-Math, 29 SAT-Math, 63 CPT-College-Level Math or 230 NGA-Advanced Algebra and Functions.
Corequisites: None.
Recommended: MATH 126 is recommended for business and social science majors
Course Category: Liberal Arts | Mathematics
This course counts toward Schoolcraft’s General Education Requirements.
This course counts toward a Michigan Transfer Agreement General Education Requirement.
This Course is Typically Offered: Winter, Spring, Fall
Check Course Availability
Course Competencies
- Solve linear, radical and absolute value equations algebraically or graphically.
- Solve polynomial and rational equations algebraically or graphically.
- Solve exponential and logarithmic equations algebraically or graphically.
- Solve linear and absolute value inequalities algebraically or graphically.
- Solve polynomial and rational inequalities algebraically or graphically.
- Sketch graphs of basic functions without the calculator (linear, square, cubic, square root, cube root, absolute value and reciprocal) showing the basic shape of the graph and labeling several plot points to include any x and y intercepts.
- Apply the standard geometric transformations of stretching, shrinking and translating to the basic functions.
- Justify graphs as even or odd by equations and by the graph.
- Determine the domain and range for graphs of functions.
- Determine intervals where a graph for a function is increasing, decreasing or constant.
- Identify local maxima and local minima from graphs of functions.
- Calculate sum, difference, product, quotient and composition of functions including their domain.
- Determine the inverse of a function numerically, algebraically and graphically.
- Graph polynomial functions including the key characteristics.
- Identify real and complex zeroes of a polynomial function by factoring and using synthetic division.
- Graph rational functions including the key characteristics.
- Graph exponential functions and logarithmic functions including the key characteristics.
- Solve application problems using linear and non-linear models (nonlinear may include polynomial, rational, exponential or logarithmic models).
- Construct mathematical models in equation or function form to solve a problem.
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MATH 129 - Precalculus
Credits: 5
Lecture Contact Hours: 5
Description: Topics covered in this course include the function concept, polynomial, rational, exponential, logarithmic, rapid review of trigonometric and inverse trigonometric functions, solving equations, curve sketching, complex numbers, coordinate geometry and conic sections. The prevailing theme is applications and graphical solutions.
Prerequisites: MATH 113 with a minimum grade of 2.0 and MATH 119 with a minimum grade of 2.0 or Minimum score of 23 ACT-Math, 29 SAT-Math, 63 CPT-College-Level Math or 260 NGA-Advanced Algebra and Functions.
Corequisites: None.
Recommended: MATH 129 is recommended for engineering, science and math majors.
Course Category: Liberal Arts | Mathematics
This course counts toward Schoolcraft’s General Education Requirements.
This course counts toward a Michigan Transfer Agreement General Education Requirement.
This Course is Typically Offered: Winter, Spring, Summer, Fall
Check Course Availability
Course Competencies
- Graph the elementary functions, including linear, quadratic, cubic, absolute value, square root, cube root and reciprocal functions, without a calculator.
- Apply the standard geometric transformations of stretching, shrinking and translating to the elementary functions.
- Solve algebraically and geometrically, equations and inequalities in one variable of the following types: linear, quadratic, polynomial, rational, exponential, logarithmic, trigonometric.
- Construct mathematical models to solve application problems.
- Determine domain and range of a function.
- Determine maximum and minimum values of a function.
- Determine intervals where a function is increasing, decreasing or constant.
- Determine algebraically and geometrically, whether a function is even, odd or neither.
- Determine the asymptotes of a function.
- Explore end behavior of a function geometrically.
- Calculate sum, difference, product and quotient of complex numbers.
- Determine real and complex zeros of a polynomial function.
- Graph exponential and logarithmic functions manually and using the graphing calculator.
- Apply geometric transformations to exponential and logarithmic functions.
- Graph trigonometric functions manually and using the graphing calculator.
- Apply geometric transformations to trigonometric functions.
- Identify conic sections.
- Graph conic sections showing key characteristics.
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MATH 135 - Finite Mathematics
Credits: 4
Lecture Contact Hours: 4
Description: Matrices and their applications to linear equations and linear programming, the simplex method, elementary probability and mathematics of finance are the topics included in this course.
Prerequisites: MATH 126 with a minimum grade of 2.0 or a minimum score of 23 ACT-Math, 29 SAT-Math, 103 CPT-College-Level Math or 250 NGA-Advanced Algebra and Functions.
Corequisites: None.
Recommended: None.
Course Category: Liberal Arts | Mathematics
This course counts toward Schoolcraft’s General Education Requirements.
This course counts toward a Michigan Transfer Agreement General Education Requirement.
This Course is Typically Offered: Fall, Winter
Check Course Availability
Course Competencies
- Graph a system of one or more linear equations in two variables in the Cartesian plane.
- Determine the solution set of a linear system of several equations and variables by using the Gaussian elimination method.
- Compute matrix operations by hand and on a calculator, including addition, subtraction, multiplication and multiplicative inverse.
- Determine the solution of a consistent, independent linear system of several equations and variables by using the inverse of the coefficient matrix.
- Apply linear equations and matrices to a variety of practical word problems.
- Determine the optimal solution(s) of a linear programming problem in two independent variables by using the graphical method.
- Determine an optimal solution of a linear programming problem in several independent variables by using the simplex tableau method, including duality.
- Analyze the marginal behavior of a linear programming problem at its optimal solution.
- Apply linear programming methods to a variety of practical word problems.
- Compute the number of outcomes for a given event by using a tree diagram.
- Compute the number of elements in a given set by using a Venn diagram and such concepts as union and intersection.
- Compute the number of outcomes for a given event by using the addition and multiplication principles, complement rule, factorials, permutations, combinations and multinomials.
- Compute the power of any binomial by using Newton’s method.
- Determine the probability of an event by counting the number of possible outcomes and using the classical definition of probability.
- Determine the probability of an event based on known probabilities by using the addition and multiplication principles and the complement rule.
- Determine the conditional probability of an event given another event by using the defining formula for conditional probability.
- Determine the conditional probability of an event given another event by using Bayes’ Theorem.
- Determine whether two events are independent based on their probabilities.
- Translate between the present and future value of a lump sum in an account earning simple or compound interest.
- Translate between the deposit amount and future value for a deposit annuity.
- Translate between the withdrawal amount and present value for a withdrawal annuity.
- Compute the payment amount or the outstanding debt for a first-time mortgage or a refinancing.
- Compute the finance charges for a loan using the add-on method.
- Compute the APR for a loan with discount points.
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MATH 145 - Calculus for Business and Social Science
Credits: 4
Lecture Contact Hours: 4
Description: The main topics of this course are differentiation of algebraic, exponential and logarithmic functions; curve sketching; optimization; constrained optimization; integration; introduction to functions of several variables; and applications.
Prerequisites: MATH 126 with a minimum grade of 2.0 or a minimum score of 23 ACT-Math, 29 SAT-Math, 103 CPT-College-Level Math or 250 NGA-Advanced Algebra and Functions.
Corequisites: None.
Recommended: None.
Course Category: Liberal Arts | Mathematics
This course counts toward Schoolcraft’s General Education Requirements.
This course counts toward a Michigan Transfer Agreement General Education Requirement.
This Course is Typically Offered: Winter, Spring, Fall
Check Course Availability
Course Competencies
- Solve a variety of practical problems, including but not limited to, problems of production, growth, decay and compound interest, using algebraic, exponential and logarithmic functions.
- Compare the concepts of limit and derivative of a function verbally, graphically, numerically or analytically.
- Compute manually the precise derivatives of algebraic, exponential and logarithmic functions at selected points.
- Interpret the meanings of the precise derivatives of algebraic, exponential and logarithmic functions at selected points.
- Determine an estimate for the derivative of any smooth function at a selected point via numerical approximation on a calculator.
- Interpret the meaning of an estimate for the derivative of any smooth function at a selected point via numerical approximation on a calculator.
- Apply methods of differentiation to solve a variety of practical problems, including but not limited to, problems of optimization.
- Compare the concepts of limit and integral of a function verbally, graphically, numerically or analytically.
- Compute manually the precise definite integrals of algebraic, exponential and logarithmic functions between selected points.
- Interpret the meanings of the precise definite integrals of algebraic, exponential and logarithmic functions between selected points.
- Determine an estimate for the definite integral of any smooth function between selected points via numerical approximation on a calculator.
- Interpret the meaning of an estimate for the definite integral of any smooth function between selected points via numerical approximation on a calculator.
- Apply methods of integration to solve a variety of practical problems, including but not limited to, problems of accumulated income.
- Compute manually the precise partial derivatives of algebraic, exponential and logarithmic function of several variables at selected points.
- Interpret the meanings of the precise partial derivatives of algebraic, exponential and logarithmic functions of several variables at selected points.
- Apply methods of partial differentiation to solve practical problems of constrained optimization.
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MATH 150 - Calculus with Analytic Geometry 1
Credits: 5
Lecture Contact Hours: 5
Description: This course is oriented to engineering, science and mathematics majors. Limits and continuity, derivatives and integrals of algebraic and some trigonometric functions, curve sketching with the aid of the graphing calculator and applications are the topics covered in this course.
Prerequisites: MATH 129 with a minimum grade of 2.0 or a minimum score of 23 ACT-Math, 29 SAT-Math, 103 CPT-College-Level Math or 280 NGA-Advanced Algebra and Functions.
Corequisites: None.
Recommended: None.
Course Category: Liberal Arts | Mathematics
This course counts toward Schoolcraft’s General Education Requirements.
This course counts toward a Michigan Transfer Agreement General Education Requirement.
This Course is Typically Offered: Winter, Spring, Fall
Check Course Availability
Course Competencies
- Investigate the concept of a limit.
- Compute limits geometrically, numerically and analytically.
- Investigate the concept of continuity geometrically and analytically.
- Determine whether or not a function is continuous at a point or overall.
- Investigate the meaning of differentiation geometrically, numerically and analytically.
- Evaluate a derivative using techniques of differentiation, including the difference quotient, the power rule, product rule, quotient rule, chain rule and implicit differentiation.
- Determine the equation of the tangent line using the derivative.
- Solve related rate problems.
- Use differentials to approximate related rates and their applications.
- Evaluate the derivative of elementary transcendental functions including logarithmic, exponential and trigonometric functions.
- Graph elementary functions using calculus techniques.
- Solve optimization problems.
- Compute the area under the curve using finite rectangles and infinite rectangles.
- Compute the area under the curve using integration.
- Compute the definite integral using the Fundamental Theorem of Calculus and Substitution Method.
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MATH 151 - Calculus with Analytic Geometry 2
Credits: 5
Lecture Contact Hours: 5
Description: This course includes the study of derivatives and integrals of transcendental functions, techniques of integration, indeterminate forms, improper integrals, infinite series, conics, polar coordinates and applications.
Prerequisites: MATH 150 with a minimum grade of 2.0.
Corequisites: None.
Recommended: MATH 230 may be taken concurrently.
Course Category: Liberal Arts | Mathematics
This course counts toward Schoolcraft’s General Education Requirements.
This course counts toward a Michigan Transfer Agreement General Education Requirement.
This Course is Typically Offered: Winter, Spring, Fall
Check Course Availability
Course Competencies
- Apply the definite integral in computing areas and surface areas.
- Apply the definite integral in computing volumes.
- Determine the derivative of hyperbolic and inverse hyperbolic functions.
- Evaluate the integral of a rational function using long division and/or partial fraction decomposition.
- Evaluate integrals using various techniques such as: parts, rationalizing substitutions, trigonometric substitution, completing the square.
- Evaluate improper integrals.
- Identify convergence or divergence of various sequences.
- Identify convergence or divergence of an infinite series using an appropriate test.
- Investigate the limit of a geometric, telescoping, alternating or p-series.
- Determine the interval of convergence for a power series.
- Determine a power series representation of various functions.
- Approximate certain non-polynomial function values and definite integrals using power series.
- Compute the arc length of a parametric or polar curve.
- Compute the slope of a tangent line to a parametric or polar curve.
- Compute the area of a region enclosed by polar curves.
- Analyze conic sections.
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MATH 230 - Linear Algebra
Credits: 4
Lecture Contact Hours: 4
Description: Topics covered in this course include systems of linear equations, matrices, determinants, Euclidean vector spaces, general vector spaces, inner product spaces, eigenvalues and eigenvectors, diagonalization, linear transformations and applications.
Prerequisites: MATH 150 with a minimum grade of 2.0
Corequisites: None.
Recommended: None.
Course Category: Liberal Arts | Mathematics
This course counts toward Schoolcraft’s General Education Requirements.
This course counts toward a Michigan Transfer Agreement General Education Requirement.
This Course is Typically Offered: Fall, Winter
Check Course Availability
Course Competencies
- Calculate an expression involving matrix operations including addition, subtraction, multiplication, scalar-multiplication, and transposition.
- Calculate the determinant of a given matrix using various techniques including cofactor expansion, row reduction, and shortcuts for small or triangular matrices.
- Calculate the multiplicative inverse of a given square matrix using various techniques including Gauss-Jordan Elimination and the adjoint-determinant method.
- Determine the solution of a system of linear equations using various techniques including Gauss, Gauss-Jordan, matrix-inverse, and Cramer methods.
- Calculate an expression involving vector operations, including addition, subtraction, scalar-multiplication, dot-multiplication, cross-multiplication, magnitudes, and parallel and perpendicular projections.
- Figure out equations for a line or plane in three-dimensional Euclidean space, given certain facts about the line or plane.
- Determine whether a given set of objects and operations constitute a vector space or subspace by using the relevant axioms.
- Determine whether a given set of vectors is linearly independent, whether it spans a given vector space, and whether it constitutes a basis for the vector space.
- Construct a basis for the null space of a given system of linear equations.
- Construct a basis for the linear span of a given set of vectors.
- Calculate the coordinates of a given vector relative to a given basis.
- Calculate the change-of-basis matrix for transitions from one given basis to another.
- Translate the coordinates of a given vector from one basis to another by using the change-of-basis matrix.
- Determine whether a given scalar function on a given vector space constitutes an inner product by using the relevant axioms.
- Calculate lengths, distances, and angles between vectors using a specified inner product.
- Construct an orthonormal basis for a given set of vectors in an inner product space by using the Gram-Schmidt method.
- Determine whether a given function between vector spaces constitutes a linear transformation by using the relevant axioms.
- Construct a basis for the kernel or for the range of a given linear transformation.
- Calculate the matrix that represents a given linear transformation relative to a given pair of bases.
- Calculate the values of a given linear transformation (or of its inverse) by using the matrix that represents it.
- Determine the eigenvalues and eigenvectors of a given linear transformation or matrix.
- Determine a diagonalized or orthogonally diagonalized form for a given linear transformation or matrix.
- Calculate powers of a given square matrix by using a diagonalized or orthogonally diagonalized form.
- Apply matrix methods to solve selected types of practical problems involving networks, curve-fitting, directed graphs, Markov chains, linear differential equations, conic sections, or quadric surfaces.
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MATH 240 - Calculus With Analytic Geometry 3
Credits: 5
Lecture Contact Hours: 5
Description: Vectors in the plane, vectors in three-space, solid analytic geometry, partial derivatives, line integrals, multiple integrals and applications are the topics covered in this course.
Prerequisites: MATH 151 with a minimum grade of 2.0.
Corequisites: None.
Recommended: None.
Course Category: Liberal Arts | Mathematics
This course counts toward Schoolcraft’s General Education Requirements.
This course counts toward a Michigan Transfer Agreement General Education Requirement.
This Course is Typically Offered: Winter, Spring, Fall
Check Course Availability
Course Competencies
- Calculate operations involving vectors.
- Apply vectors to physical situations in the plane.
- Apply vectors to physical situations, including motion, in three dimensions.
- Calculate limits for multivariable functions.
- Determine continuity for multivariable functions.
- Evaluate partial derivatives for multivariable functions.
- Evaluate mixed partial derivatives for multivariable functions.
- Optimize functions of two variables.
- Evaluate double integrals in rectangular coordinates.
- Evaluate double integrals in polar coordinates.
- Evaluate triple integrals in rectangular coordinates.
- Evaluate triple integrals in cylindrical coordinates.
- Evaluate triple integrals in spherical coordinates.
- Evaluate line integrals.
- Apply vector calculus to physical situations.
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MATH 252 - Differential Equations
Credits: 5
Lecture Contact Hours: 5
Description: Topics covered in this course include first order differential equations, second order linear equations, series solutions of second order linear equations, higher order linear equations, Laplace transform, systems of first order linear equations, numerical methods and qualitative theory of differential equations.
Prerequisites: MATH 240 with a minimum grade of 2.0.
Corequisites: None.
Recommended: None.
Course Category: Liberal Arts | Mathematics
This course counts toward Schoolcraft’s General Education Requirements.
This course counts toward a Michigan Transfer Agreement General Education Requirement.
This Course is Typically Offered: Fall, Winter
Check Course Availability
Course Competencies
- Model a mechanical oscillator.
- Model a series or parallel electrical circuit of the RLC (resistor, inductor, capacitor) type.
- Model one population in conditions of natural growth or decay, logistic growth, explosion, or extinction.
- Model two populations in conditions of predation or competition.
- Sketch graphical solutions of a first-order differential equation by hand using the slope field.
- Determine the general solution of a simple first-order differential equation using such techniques as separation of variables, integrating factors, and substitution methods.
- Compute the approximate solution of a first-order initial-value differential equation using a numerical method (Euler, Runge-Kutta, etc.) by hand or with a calculating device.
- Determine the general solution of a homogeneous constant-coefficient linear differential equation by using the Characteristic Polynomial method.
- Determine the general solution of a nonhomogeneous constant-coefficient linear differential equation by using the Undetermined Coefficients or Variation of Parameters method.
- Determine the general solution of a system of linear differential equations by finding its real or complex eigenvalues and eigenvectors.
- Identify graphically the location, type, and stability of all critical points in a given phase-plane diagram.
- Determine analytically the location, type, and stability of all critical points by finding the eigenvalues of the linearized system.
- Determine the Laplace transform of various simple functions by hand.
- Determine the Laplace transform of various continuous, piecewise-continuous, or periodic functions with the aid of a table.
- Determine the inverse Laplace transform of various functions with the aid of a table.
- Solve differential equations by the Laplace transform method.
- Determine power series solutions of a differential equation and their radii of convergence.
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