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Course Criteria
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3.00 Credits
3 hours lecture per week Prerequisite(s): A grade of "A" in MATH 24, a grade of "C" or higher in MATH 25, a grade of "C" or higher in MATH 81, or Placement Test recommendation of MATH 100 or higher; qualification for ENG MATH 111 is designed to give prospective elementary education majors the depth of understanding necessary to teach mathematics in the elementary classroom. Topics will include numbers, operations on sets, patterns, functions and algebra. 8 Emphasis will be on understanding, communication, problem solving, representing mathematical ideas, and reasoning and proof. Upon successful completion of MATH 111, the student should be able to: Explain ways of representing numbers, relationships among numbers, and number systems. Perform various operations on sets; union, intersection, etc. Identify and describe various types of patterns and functional relationships. Use symbolic forms to represent, model, and analyze mathematical situations. Solve a variety of problems. Communicate mathematical ideas verbally, in writing, and through mathematical representations to various audiences. Apply appropriate mathematical reasoning to justify solution paths to various problems.
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3.00 Credits
3 hours lecture per week Prerequisite(s): A grade of "C" or higher in MATH 111. MATH 112 is the designed to give prospective elementary education majors the depth of understanding necessary to teach mathematics in the elementary classroom. Topics will include representations of and operations on the natural numbers, integers, rational numbers and real numbers, and properties of those operations. Emphasis will be on communication, connections to other parts of mathematics, problem solving, representations, and reasoning and proof. Upon successful completion of MATH 112, the student should be able to: Demonstrate various representations of Natural numbers and Integers. Define the operations on Natural numbers and Integers. Identify, describe, and demonstrate the proper use of the properties of operations on Natural numbers and Integers. Demonstrate various representations of Rational and Real numbers. Define the operations on Rational and Real numbers . Identify, describe, and demonstrate the proper use of the properties of operations on Rational and Real numbers. Apply appropriate mathematical reasoning to justify solution paths to various problems. · Solve a variety of problems. · Communicate mathematical ideas verbally, in writing, and through mathematical representations to various audiences. · Demonstrate mathematical literacy and fluency.
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3.00 Credits
3 hours lecture per week Prerequisite(s): A grade of "C" or higher in MATH 25 or higher, or placement at MATH 100 or higher level mathematics course; qualification for ENG 22 or ESOL 94 or higher level English course. MATH 115 covers elementary probability and statistics including standard deviation, calculations and inferences about means and proportions, normal distributions and linear correlation. Upon successful completion MATH 115, the student should be able to: Describe and interpret various descriptive statistics such as mean, median, mode, range, standard deviation and quartiles. Draw and interpret various graphs such as frequency histograms, bar graphs, and boxplots. Solve problems involving the probability of events. Calculate probabilities involving normal random variables and categorical data. Determine and interpret (for large samples) confidence interval estimates of population means and proportions. Conduct hypothesis tests using z and chi-square about means and proportions of populations. 9 For a set of paired data, produce a scatter plot, find the regression line, and find and interpret the correlation coefficient.
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3.00 Credits
3 hours lecture per week Prerequisite(s): A grade of "C" or higher in MATH 103, or a grade of "C" or higher in MATH 27, or qualification for MATH 135 on math placement tes MATH 135 focuses on elementary functions and graphs, polynomials, systems of linear equations, absolute values, inequalities, logarithms and exponentials. Upon successful completion of MATH 135, the student should be able to: Apply definitions of functions, inverse functions and composition functions correctly. Show familiarity with all principles involving linear functions. Find roots, evaluate, sketch, and solve inequalities involving polynomial functions. Graph rational functions using the concept of asymptotes. Apply definitions and principles of logarithmic and exponential functions correctly. Use knowledge and techniques of this course in solving applied problems.
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3.00 Credits
3 hours lecture per week Prerequisite(s): A grade of "C" or higher in MATH 135 or qualification for MATH 140 on math placement test. MATH 140 covers inverse functions, plane trigonometry, polar coordinates, conic sections and vectors. Upon successful completion of MATH 140, the student should be able to: Solve verbal and non-verbal problems in plane trigonometry. Relate functional and geometric properties of conic sections. Simplify algebraic expressions involving complex numbers. Relate vectors with circular functions.
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3.00 Credits
3 hours lecture per week Prerequisite(s): A grade of "C" or higher in MATH 135 or placement recommendation of MATH 140. MATH 203 covers the mathematics of finance - annuities, perpetuities, present value, derivatives, integrals, graphical analysis, and mathematical models as applied to business. MATH 203 also covers applications of the derivative to curve sketching and the solutions of optimization problems, and involves the algebra and geometry of linear, quadratic, polynomial, exponential, and logarithmic functions, including functions of more than one variable. Upon successful completion of MATH 203, the student should be able to: Apply the concepts of function, limits, and continuity to business and financial problems. Compute the derivatives and integrals of power functions, exponential, logarithmic functions and any combination of these functions. Apply the derivative to problems involving slopes, tangent lines, rates of changes, and optomization. Apply the concepts of limits and derivatives to graphing. Apply the derivative and integral in solving applied problems by using more than one variable.
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4.00 Credits
4 hours lecture per week Prerequisite(s): A grade of "C" or higher in MATH 140 or equivalent or satisfactory performance on the math placement test. MATH 205 focuses on basic concepts, limits and continuity, techniques and applications of differentiation, introduction to integration. Upon successful completion of MATH 205, the student should be able to: Understand and apply the concept of limit. Differentiate polynomial functions and sums, products, quotients, roots, and compositions of polynomial functions. Use differential calculus to sketch curves and to solve applied problems. 0 Integrate functions by approximation and by use of antiderivatives. Use integral calculus to determine area and to solve applied problems.
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4.00 Credits
4 hours lecture per week Prerequisite(s): A grade of "C" or higher in MATH 205 or equivalent. MATH 206 is the second course in the calculus sequence, which focuses on techniques of integration and on integrals of specific functions and their applications. Explores infinite series. Upon successful completion of MATH 206, the student should be able to: Differentiate and integrate elementary transcendental functions. Integrate functions using special methods. Apply L'Hospital's Rule and evaluate improper integrals. Determine the convergence of infinite sequences and series and approximate functions with Taylor polynomials. Use the techniques developed in this course to solve applied problems.
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1.00 Credits
3 hours lab per week Corequisite(s): MATH 206. MATH 206L is an introduction to mathematics computer software for solving calculus problems, graphing functions, and gaining a better understanding (graphically and numerically) of calculus concepts. No prior knowledge of computers is required. Upon successful completion of MATH 206L, the student should be able to use symbolic mathematics computer software to find: Solutions of equations and systems of equations. First and second derivatives. Estimates of function zeros using Newton's Method. Definite and indefinite integrals. Estimates of definite integrals using numerical methods. Taylor polynomials and estimate their remainders. The convergence or divergence of infinite series.and should have insights into the fundamental calculus concepts of: Limit of a function. Derivative of a function. Application of Newton's Method. Definite integral. Numerical methods for estimating the definite integral. Convergence of Taylor polynomials. Solutions of differential equations of the form F'(x)=G(x,y).
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4.00 Credits
4 lecture hours per week Prerequisite(s): A grade of "C" or higher in MATH 206. MATH 231 is the third course in the calculus sequence, which focuses on functions of several variables using a vector oriented approach. The course also studies partial differentiation. Upon successful completion of MATH 231, the student should: Acquire the ability to use differential calculus on functions of several variables of mathematics. Be able to differentiate functions of several variables and use the derivative to solve problems. Be exposed to and acquire some knowledge of the methods and logic of mathematics. Acquire an understanding of what a limit is and of the properties of limits of vector functions.
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