 # Mathematics --- MATH

Department Homepage: https://inverhills.edu/DegreesAndPrograms/Mathematics/

### MATH 0740  Prealgebra   4.0 crCourse Outline for MATH 0740

Integrates topics of algebra throughout, including simplifying expressions and solving equations. Covers: operations with and properties of signed rational numbers; conversion between fractions, decimals, and percents; estimation; exponents; order of operations; ratios, rates, and proportions; descriptive statistics; interpretation of data from charts, tables, and graphs; US & metric measures and conversions; square roots; similarity; perimeter, area, and volume of geometric shapes; applications; graphing linear equations by point-plotting; and positive and negative slope. Prereq: Recommendation based on the results of the Inver Hills Assessment Inventory or a grade of C or higher in MATH 0640.

### MATH 0840  Introductory Algebra   4.0 crCourse Outline for MATH 0840

Designed for students who need work in beginning algebra and who are preparing for Intermediate Algebra (0940), Introduction to Statistics (1103), Math for Liberal Arts (1101), or Mathematical Foundations (1107). The topics in this course include real number operations and properties; solving linear equations and inequalities; graphing linear equations; rules of exponents; polynomial operations; factoring polynomials; solving quadratic equations by factoring and with quadratic formula; solving systems of linear equations; functions; applications are embedded throughout the course. Recommendation based on the results of the Inver Hills Assessment Test within the last 2 years. This course will not fulfill any degree requirements.

### MATH 0880  Intensive Introductory and Intermediate Algebra   4.0 crCourse Outline for MATH 0880

Is a fast-paced review of algebra skills designed ONLY for students who have previously learned elementary and intermediate algebra, but who need a refresher. This is a web supplemented course. Students must be highly motivated, independent learners and can expect to spend at least 25 hours per week completing homework outside of class. Students will complete assignments online using mathematics software and take a written midterm and final exam in both 0840 and 0940. Successful students will complete both 0840 and 0940 in one semester. For course topics please refer to the descriptions for MATH0840 and MATH0940. This course will not fulfill any degree requirements.

### MATH 0940  Intermediate Algebra   5.0 crCourse Outline for MATH 0940

Prepares students for course work in College Algebra (1118) or Pre-Calculus (1127). Course topics include graphing linear, quadratic, absolute value, square root, exponential and logarithmic functions using transformations; graphing piecewise-defined functions; factoring polynomials; solving polynomial, rational, radical, exponential, logarithmic equations and applied problems; the arithmetic of rational expressions and radical expressions; simplifying rational and radical expressions. Recommendation based on the results of the Inver Hills Assessment Test or grade of C or higher in MATH 0840 within the last 2 years.

### MATH 1101  Math for Liberal Arts   3.0 crCourse Outline for MATH 1101

Gives non-mathematicians an appreciation of mathematical ideas and the power and utility of mathematical skills in the modern world. Topics will be selected from: voting and weighted voting systems, fair division and apportionment; routing, minimum network and scheduling problems; mathematical growth and math of finance; descriptive statistics and data analysis; basic probability and normal distributions. Placement into Read 93/94 or a grade of C or higher in Read 90 within the last 3 years.

### MATH 1103  Introduction to Statistics   4.0 crCourse Outline for MATH 1103

Presents basic statistics which includes descriptive and graphical statistics, basic probability, probability distributions, sampling distributions, confidence intervals and hypotheses testing for one or two populations, linear regression, chi-square tests, and ANOVA. Professional statistical software, such as Minitab, will be integrated throughout the class. Graphing calculator required for the course. Recommendation based on the results of the Inver Hills Assessment Test or grade of "C" or higher in MATH 0820 or 0840 within the last 2 years.

### MATH 1107  Mathematical Foundations   4.0 crCourse Outline for MATH 1107

Includes the topics: analysis of the problem solving process; sets and number systems; operations, properties, and computation with the real numbers and their classic subsets; number theory; decimals, ratio, proportion, and percents; statistics; probability; measurement; relations, functions and patterns; algebra models; geometric shapes; and applications. This course can be used for prospective elementary education majors and liberal arts students. This course meets the Minnesota Professional Educator Licensing and Standards Board (PELSB) 8710.3200, Subp. 3, Standard H1 a, b, c, H2 a, b, H3 a, b, c, d, H4 a, b, H5 a, b, H6 a, b, H7 a, b, c, d. Prerequisite: Recommendation based on the results of the Inver Hills Assessment Test or grade of "C" or higher in MATH 0840 within the last 2 years.

### MATH 1118  College Algebra I   4.0 crCourse Outline for MATH 1118

Prepares students for Calculus I (MATH 1133) when taken in sequence with MATH 1119 or for Survey of Calculus (MATH 1120). Topics include the study of algebraic, exponential, and logarithmic functions; graphing functions using transformations; inverse functions; polynomial, exponential, logarithmic equations; systems of linear and non-linear equations; applied problems; building models from data. Use of technology will be embedded throughout the course. Recommendation based on the results of the Inver Hills Assessment Test or grade of C or higher in MATH 0940 or MATH 0880 within the last 2 years.

### MATH 1119  College Algebra II   4.0 crCourse Outline for MATH 1119

Prepares students for Calculus I (MATH 1133) when taken in sequence with College Algebra I (MATH 1118). Topics include trigonometric functions and their graphs, trigonometric identities and applications, law of sines and cosines, solving trigonometric and parametric equations, conic sections, polar coordinates and graphing functions in polar form, vectors and the complex plane. Use of technology will be embedded throughout the course.

### MATH 1120  Survey of Calculus   3.0 crCourse Outline for MATH 1120

Provides students with a survey of topics from differential and integral calculus. This course is not intended as a prerequisite for other courses in calculus. Topics include functions and limits; differentiation of algebraic, exponential, and logarithmic functions; basic integration including the substitution method. Applications include graphing functions, optimization problems, related rates, growth and decay models, and area under curves. Applications are drawn from the life and physical sciences, business and economics, and the social sciences. Recommendation based on the Inver Hills Assessment Test results or grade of C or higher in MATH 1118 or MATH 1127 within the last 2 years.

### MATH 1127  PreCalculus   5.0 crCourse Outline for MATH 1127

Prepares students for Calculus I (MATH 1133). Topics include the study of algebraic, exponential, logarithmic, and trigonometric functions; graphing functions using transformations; inverse functions; polynomial, exponential, logarithmic, and trigonometric equations; applied problems; trigonometric identities. Time permitting, building models from data may be included. Use of technology will be embedded throughout the course. Recommendation based on the Inver Hills Assessment Test results or grade of B or higher in MATH 0940 or MATH 0880 within the last 2 years.

### MATH 1133  Calculus I   5.0 crCourse Outline for MATH 1133

Provides an introduction to single variable calculus and prepares students for Calculus II (MATH 1134). The topics include limits, derivatives (including trigonometric, logarithmic and exponential functions), continuity, applications of derivatives to related rates and optimization, graphing using information from the first and second derivatives, separable differential equations, Riemann Sums, basic integration techniques (including substitution), definite integrals, the Fundamental Theorem of Calculus, Trapezoidal and Simpson's Rule. Students will become proficient with a computer algebra system. Use of technology will be embedded throughout the course. Recommendation based on the Inver Hills Assessment Test results or grade of "C" or higher in MATH 1127 or MATH 1119 within the last 2 years.

### MATH 1134  Calculus II   5.0 crCourse Outline for MATH 1134

Prepares students for Multivariable Calculus (MATH 2219). Is the second course in the two-semester sequence of single variable calculus. The topics include applications of the integral: area, volume, surface area, center of mass, work, liquid pressure and arc length; techniques of integration; improper integrals; conics; calculus in polar coordinates; calculus involving parametrically-defined curves; and infinite series. Familiarity with a computer algebra system is expected. Use of technology will be embedded throughout the course.

### MATH 2219  Multivariable Calculus   5.0 crCourse Outline for MATH 2219

Extends concepts of single-variable calculus to calculus of several variables. The topics include vectors in three-dimensional space, quadric surfaces, limits in two and three dimensions, partial derivatives, gradients, extreme value problems, multiple integration and applications, space curves, curvature, The Frenet frame, divergence, curl, line integrals, conservative vector fields and potential functions, surface and volume integrals, Green's, Stokes' and the Divergence Theorems. Knowledge of a computer algebra system is expected. Use of technology will be embedded throughout the course.

### MATH 2221  Introduction to Linear Algebra   3.0 crCourse Outline for MATH 2221

Provides an introduction to linear algebra topics including: systems of linear equations, matrices, determinants, vector spaces, linear transformations, eigenvalues and eigenvectors, and selected applications. Familiarity with a computer algebra system is expected. Use of technology will be embedded throughout the course.

### MATH 2222  Introduction to Differential Equations   3.0 crCourse Outline for MATH 2222

Provides an introduction to ordinary differential equations.Topics include basic definitions, concepts and terminology of ordinary differential equations. Techniques of problem solving are emphasized. Specific topics covered include: solutions and applications of first-order differential equations, solutions of linear differential equations of higher order, applications of second-order linear differential equations, power series solutions, the Laplace transform, systems of linear differential equations, and an introduction to numerical and graphical methods of solution. Familiarity with a computer algebra system is expected. Use of technology will be embedded throughout the course.

### MATH 2223  Linear Algebra and Differential Equations   5.0 crCourse Outline for MATH 2223

Provides an introduction to linear algebra and ordinary differential equation topics including: systems of linear equations, matrices, determinants, vector spaces, linear transformations, eigenvalues and eigenvectors, basic concepts and terminology of ordinary differential equations, solutions and applications of first-order differential equations, solutions of linear differential equations of higher-order, applications of second-order differential equations, the Laplace transform, systems of linear differential equations, and an introduction to numerical and graphical methods of solution. Techniques of problem solving are emphasized. Familiarity with a computer algebra system is expected. Use of technology will be embedded throughout the course.