Real numbers and their properties, first degree equations and inequalities, graphs of linear equations in two variables, systems of linear equations in two variables, properties of integer exponents, polynomial operations, basic factoring, rational expressions, radical expressions, quadratic equations, and applied problems and problem solving.
A student who successfully completes the course will be able to:
Simplify expressions and solve equations of the following types: linear, quadratic, rational, and radical.
Interpret and construct linear graphs.
Translate, model, and solve applied problems using linear, quadratic, rational, and radical equations.
Logically present clear, complete, accurate, and sufficiently detailed solutions to communicate reasoning and demonstrate the method of solving problems.
Study of points, lines, angles, polygons, triangles, similarity, congruence, geometric proofs, area, volume, perimeter, the circle, right triangle trigonometry.
A student who successfully completes the course will be able to:
Logically present clear, complete, accurate, and sufficiently detailed solutions to communicate reasoning and demonstrate the method of solving problems.
Construct deductively valid proofs of theorems by using definitions, postulates, and previously proven theorems.
Using a compass and straightedge construct standard geometric figures: duplicated angle, duplicated line segment, angle bisector, perpendicular bisector, equilateral triangle, square, and the incenter, circumcenter, orthocenter, and centroid of a triangle.
Exponents, radicals, complex numbers, factoring, linear and quadratic equations and inequalities; linear, quadratic, exponential and logarithmic functions; graphing, and systems of equations.
A student who successfully completes the course will be able to:
Simplify expressions and solve equations of the following types: linear, quadratic (including some with complex solutions), rational, radical, absolute value, exponential, and logarithmic.
Interpret and construct graphs of linear, quadratic, exponential, and logarithmic functions and their inverse functions.
Practical Mathematics is a one semester course for non-math, non-science majors covering the topics of numeracy, proportional reasoning, algebraic reasoning, trigonometric reasoning, data analysis and critical thinking through real world applications. Students develop the skills needed to apply mathematical and technological skills and procedures to analyze and interpret mathematical data. Algebraic, geometric and trigonometric topics covered include: real numbers and their properties; proportions; measurement of lengths, areas and volumes; first degree equations and inequalities; functional analysis; graphs of linear, quadratic, and exponential equations; systems of equations in two variables; quadratic, exponential, and logarithmic equations; and basic right triangle trigonometry. <b>Not intended for students on the calculus track.
A student who successfully completes the course will be able to:
Apply the concept of numeracy in multiple contexts.
Recognize proportional relationships and use proportional reasoning to solve problems.
Use algebra to recognize and write relationships involving variables; interpret those relationships and solve problems.
Apply basic right triangle trigonometry to analyze data, write equations and solve applied problems.
Analyze and interpret data critically in multiple formats including graphs, tables, equations, formulas and words.
Develop the ability to think critically and solve problems in a variety of contexts using the tools of mathematics including technology.
B-STEM Intermediate Algebra is a one semester course for business, science, technology, engineering and math majors covering the topics of linear equations and applications, absolute value equations and inequalities, factoring, operations on rational and radical expressions, functions including composition and inverses, quadratic functions and graphs, exponential and logarithmic expressions and equations, and systems of equations. Computational techniques developed in beginning algebra are prerequisite skills for this course. This course is appropriate for students on a business or STEM pathway and have some knowledge of beginning algebra or who have had at least two years of high school algebra but have not used it for several years.
Just in time support option covering the core prerequisite skills, competencies, and concepts for Intermediate Algebra. Intended for students who are concurrently enrolled in MATH G - B-STEM Intermediate Algebra. Topics include: numeracy, computational skills, the vocabulary of algebra, evaluation of expressions and functions, solving and graphing linear equations and inequalities in one and two variables, solving and graphing systems of equations in two variables, factoring, algebraic operations on polynomial and rational expressions. Recommended for students taking Math G – B-STEM Intermediate Algebra with little or no recent algebra knowledge.
Everyone! Training your brain to solve problems will help prepare you for challenges you face in your classes, but also challenges you face in your job and in life.
Individual and small-group problem solving geared toward real life situations and nontraditional problems. Problem solving strategies include: draw a diagram, eliminate possibilities, make a systematic list, look for a pattern, guess and check, solve an easier related problem, subproblems, use manipulatives, work backward, act it out, unit analysis, use algebra, finite differences, and many others. Divergent thinking and technical communication skills of writing and oral presentation are enhanced. Designed to teach students to think more effectively and vastly increase their problem solving ability.
A student who successfully completes the course will be able to:
Think divergently while designing and evaluating a variety of approaches when brainstorming possible solutions to new problems from a variety of mathematical situations and other disciplines.
Develop and implement strategies for approaching unfamiliar mathematical problems from a variety of areas.
Through writing, small group work, and oral presentation, logically present clear, complete, accurate, and sufficiently detailed solutions to communicate reasoning and demonstrate the solution of problems.
Evaluate, improve, and correct the appropriateness and reasonableness of a solution to a problem that was presented orally, in small groups, or in written form.
Develop mathematical and logical communication skills in small groups, oral presentations, and writing.
Study of algebra topics beyond MATH D; including functions, graphs, logarithms, systems of equations, matrices, analytic geometry sequences, mathematical induction, and introduction to counting techniques.
A student who successfully completes the course will be able to:
Simplify expressions and solve equations of the following types: linear, quadratic (including some with complex solutions), rational, radical, absolute value, exponential, and logarithmic.
Interpret and construct graphs of quadratic, rational, exponential, logarithmic functions, and conic sections.
Translate, model, and solve applied problems utilizing linear, quadratic, rational, radical, exponential, logarithmic functions, and matrix algebra.
Logically present clear, complete, accurate, and sufficiently detailed solutions to communicate reasoning and demonstrate the method of solving problems.
Apply techniques from linear algebra and combinatorics.
Introduction to the basic concepts of statistics. Emphasis on statistical reasoning and application of statistical methods. Areas included: graphical and numerical methods of descriptive statistics; basic elements of probability and sampling; binomial, normal, and Student's t distributions; confidence intervals and hypothesis testing for one and two population means and proportions; chi-square tests for goodness-of-fit and independence; linear regression and correlation; and one-way analysis of variance (ANOVA).
A student who successfully completes the course will be able to:
Recognize, label and identify data by type and level of measurement.
Construct and interpret data using graphical and numerical methods of descriptive statistics.
Calculate and interpret problems involving basic elements of probability and sampling.
Conduct hypothesis tests and construct confidence interval estimates for population means and proportions; chi-square tests for goodness-of-fit and independence; linear regression and correlation; and one-way analysis of variance (ANOVA).
Logically present clear, complete, and sufficiently detailed solutions to demonstrate understanding and communicate reasoning of statistical methods using technology when appropriate.
Just in time support option covering the core prerequisite skills, competencies, and concepts for Elementary Statistics. Intended for students who are concurrently enrolled in MATH 13. Topics include concepts from arithmetic, pre-algebra, elementary and intermediate algebra, and descriptive statistics that are needed to understand the basics of college-level statistics. Concepts are taught through the context of descriptive data analysis including an introduction to technologies such as Desmos, Excel, Statcrunch, Minitab, SPSS or graphing calculators. Recommended for students taking MATH 13 with little or no recent algebra knowledge.
A student who successfully completes the course will be able to:
Study of set theory, relations and functions, logic, combinatorics and probability, algorithms, computability, matrix algebra, graph theory, recurrence relations, number theory including modular arithmetic. Various forms of mathematical proof are developed: proof by induction, proof by contradiction.
A student who successfully completes the course will be able to:
Logically present clear, complete, accurate, and sufficiently detailed solutions to communicate reasoning and demonstrate the method of solving problems.
Construct valid proofs of theorems using the following techniques: mathematical induction, direct and indirect proofs, by contradiction, with truth tables, and by logical equivalences.
Solve counting problems using combinatorics, recurrence relations, and generating functions.
Solve applied problems using discrete probability theory, graph theory, tree diagrams, and Boolean Algebra.
Review of functions, limits, differentiation and integration of algebraic functions, calculus for exponential and logarithmic functions, applications of calculus in social and life sciences. This course is not intended for students majoring in mathematics, engineering, physics, or chemistry.
A student who successfully completes the course will be able to:
Evaluate limits of functions using limit laws and graphical methods and utilize limits to determine continuity.
Calculate derivatives and integrals of algebraic, exponential, and logarithmic functions.
Translate, model, and solve applied problems in the social and life sciences utilizing derivatives and integrals.
Construct graphs of algebraic functions using their derivatives.
Logically present clear, complete, accurate, and sufficiently detailed solutions to communicate reasoning and demonstrate the method of solving problems.
Differentiation and integration of trigonometric functions, functions of several variables, partial derivatives, double integrals, introduction to differential equations, sequences and series, applications of calculus in the social and life sciences.
A student who successfully completes the course will be able to:
Calculate integrals of algebraic, trigonometric, inverse, and transcendental functions.
Sketch graphs of trigonometric functions using calculus techniques.
Translate, model, and solve optimization problems utilizing differentiation, partial differentiation, integration, and Lagrange multipliers.
Analyze points, surfaces, and graphs in three dimensions.
Logically present clear, complete, accurate, and sufficiently detailed solutions to communicate reasoning and demonstrate the method of solving problems.
Exploration of mathematical patterns and relations, formulation of conjectures based on the explorations, proving (or disproving) the conjectures. Includes different problem solving techniques, number theory, probability, statistics, sequences and series, and geometry. Intended for students interested in elementary education.
A student who successfully completes the course will be able to:
Develop and implement strategies for approaching unfamiliar mathematical problems.
Evaluate, improve, and correct orally presented or written solutions.
Logically present clear, complete, accurate, and sufficiently detailed solutions to communicate reasoning and demonstrate the method of solving problems
Introduces students to the art and application of mathematics in the world around them. Topics include mathematical modeling, voting and apportionment, and mathematical reasoning with applications chosen from a variety of disciplines. Not recommended for students entering elementary school teaching or business.
A student who successfully completes the course will be able to:
Solve college level math problems from a variety of different areas.
Utilize linear, quadratic, exponential, and logarithmic equations, systems of equations, and their graphs to analyze mathematical applications from various disciplines.
Analyze given information and implement strategies for solving problems involving mathematical and logical reasoning.
Use mathematical modeling as a problem solving tool in other disciplines and contexts.
Logically present clear, complete, accurate, and sufficiently detailed solutions to communicate reasoning and demonstrate the method of solving problems.
This course focuses on the development of quantitative reasoning skills through in-depth, integrated explorations of topics in mathematics, including the real number system and its subsystems. The emphasis is on comprehension and analysis of mathematical concepts and applications of logical systems.
Applications of mathematics in economics and business contexts. Topics include tables and graphs, functions, finance (interest and exponential models), rates of change including applications and optimization, and linear programming.
A student who successfully completes the course will be able to:
Apply rates of change to marginal analysis and business applications.
Logically present clear, complete, accurate, and sufficiently detailed solutions to communicate reasoning and demonstrate the method of solving business problems.
Translate, model, and solve applied business problems utilizing derivatives.
Construct and interpret graphs of polynomial, exponential, logarithmic, and composite functions; solve linear programming problems graphically.
Fundamentals of trigonometry. Topics include review of algebraic functions, definitions of trigonometric and circular functions, graphs, identities and applications. Other material includes solving trigonometric equations, solving triangles using the Laws of Sines and Cosines, vectors, polar coordinates and graphs, polar representations of complex numbers and conic sections. (Formerly Math 8)
A student who successfully completes the course will be able to:
Solve trigonometric equations and triangles. Manipulate trigonometric expressions and identities, vectors, and polar representations of complex numbers.
Interpret and construct graphs of trigonometric functions, conic sections, parametric equations, and vectors utilizing rectangular and polar coordinates.
Translate, model, and solve applied problems utilizing trigonometric functions and vectors.
Logically present clear, complete, accurate, and sufficiently detailed solutions to communicate reasoning and demonstrate the method of solving problems.
Designed for students interested in furthering their knowledge at an independent study level in an area where no specific curriculum offering is currently available. Independent study might include, but is not limited to, research papers, special subject area projects, and research projects. See Independent Study page in catalog.
Preparation for calculus. Study of polynomials, rational functions, exponential and logarithmic functions, trigonometric functions, systems of linear equations, matrices, determinants, rectangular and polar coordinates, conic sections, complex number systems, mathematical induction, binomial theorem, and sequences. Recommended for students who plan to take MATH 30.
A student who successfully completes the course will be able to:
Simplify expressions and solve equations of the following types: linear, quadratic (including some with complex solutions), rational, radical, absolute value, exponential, logarithmic, and trigonometric.
Interpret and construct graphs of polynomial, rational, exponential, logarithmic, and trigonometric functions, and conic sections.
Translate, model, and solve applied problems utilizing polynomial, rational, radical, exponential, logarithmic, trigonometric functions, and matrix algebra.
Logically present clear, complete, accurate, and sufficiently detailed solutions to communicate reasoning and demonstrate the method of solving problems.
Apply techniques from linear algebra and combinatorics.
Introduction to differential and integral calculus. Content includes limits, continuity, differentiation and integration of algebraic, trigonometric, exponential, logarithmic, hyperbolic and other transcendental functions; as well as application problems.
A student who successfully completes the course will be able to:
Evaluate limits of functions using limit laws, the definition of a limit, or L'Hospital's Rule; and utilize limits to determine continuity.
Calculate derivatives and integrals of algebraic and transcendental functions.
Translate, model, and solve applied problems utilizing derivatives and integrals.
Construct graphs of algebraic and transcendental functions using their derivatives.
Logically present clear, complete, accurate, and sufficiently detailed solutions to communicate reasoning and demonstrate the method of solving problems.
Continuation of MATH 30. Content includes techniques of integration, improper integrals, applications of integration, infinite series, parametric equations and polar coordinates.
A student who successfully completes the course will be able to:
Integrate algebraic and transcendental functions.
Construct and interpret graphs of parametric and polar equations applying appropriate calculus techniques.
Translate, model, and solve applied problems utilizing differentiation, integration, and infinite series.
Demonstrate knowledge and theory of infinite series by applying appropriate theorems to determine convergence and divergence.
Logically present clear, complete, accurate, and sufficiently detailed solutions to communicate reasoning and demonstrate the method of solving problems.
Continuation of Math 31. Vectors and analytic geometry in the plane and space; functions of several variables; partial differentiation, multiple integrals, and application problems; vector functions and their derivatives; motion in space; and surface and line integrals, Stokes' and Green's Theorems, and the Divergence Theorem.
A student who successfully completes the course will be able to:
Calculate partial derivatives and multiple integrals of multivariable functions.
Translate, model, and solve applied problems utilizing vector functions, partial derivatives, Lagrange multipliers, Second Derivative Test, Green's Theorem, Stokes' Theorem, and the Divergence Theorem.
Utilize graphs of multivariable functions to set up, evaluate, and solve double and triple integrals; including rectangular, cylindrical, and spherical coordinates.
Logically present clear, complete, accurate, and sufficiently detailed solutions to communicate reasoning and demonstrate the method of solving problems.
First and second order ordinary differential equations, linear differential equations, numerical methods and series solutions, Laplace transforms, modeling and stability theory, systems of linear differential equations, matrices, determinants, vector spaces, linear transformations, orthogonality, eigenvalues and eigenvectors.
A student who successfully completes the course will be able to:
Solve first and higher order ordinary and linear differential equations; using Laplace transformations, numerical, and series methods.
Utilize theorems from linear algebra and use matrices to solve systems of equations, including differential equations.
Utilize theorems from linear algebra to classify sets and mappings.
Logically present clear, complete, accurate, and sufficiently detailed solutions to communicate reasoning and demonstrate the method of solving problems.
Introduction to differential and integral calculus, with particular emphasis on applications in the fields of business, economics, and social sciences. Includes: concepts of a function, limits, derivatives, integrals of polynomial, exponential and logarithmic functions, optimization problems, and calculus of functions of more than one variable. <b>Not recommended for students with credit for Math 30.</b>
A student who successfully completes the course will be able to:
Evaluate limits of functions using limit laws and graphical methods.
Calculate derivatives, partial derivatives, and integrals.
Translate, model, and solve applied business problems utilizing derivatives and integrals.
Logically present clear, complete, accurate, and sufficiently detailed solutions to communicate reasoning and demonstrate the method of solving business problems.
Designed to assist students to recognize common fears and misconceptions of mathematics and develop personal strategies to overcome math and test anxiety. Specific study skills and strategies are discussed. Individual math learning styles are analyzed. (not degree applicable)
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