The theory of interest will be developed. Emphasis is placed on topics included in the financial mathematics portion of the Society of Actuaries' Financial Mathematics exam. Financial mathematics is applied to areas of financial economics important in actuarial applications. Emphasis is placed on topics included in the financial economics portion of the Society of Actuaries' Financial Mathematics exam.
This course covers special undergraduate topics in mathematics which are not taught elsewhere in the department. This course may be repeated for credit when topic is different.
Prerequisites: Departmental approval. The course prepares engineering students to be able to solve problems in the following topics in engineering applications: complex numbers and calculus of complex functions; matrix and vector algebra, linear systems of equations and matrix eigenvalue problems; vector differential and integral calculus, including integral theorems; unconstrained and constrained optimization, including linear and quadratic programming.
This course is an introduction to the theory of functions of a complex variable with basic techniques and some applications. Topics include complex numbers and the extended complex plane, elementary functions of a complex variable, differentiation, conformal mappings, contour integration, Cauchy's theorem, Cauchy's formula, Taylor and Laurent series, and residue theory.
This course is an introduction to elementary partial differential equations, with applications to physics and engineering. Heat conduction, diffusion processes, wave phenomenon, and potential theory are explored by means of Fourier analysis. This course is an introduction to transform analysis based on the theory of Fourier and Laplace integrals.
Topics include contour integration, inverse formulas, convolution methods, with application to mathematical analysis, differential equations and linear systems. Topics include a complete overview of Hilbert's axioms connection, order, parallels, congruence, continuity , convex geometry convex hull, extreme points, linear programming , and projective geometry collineation, coordination, the Main Theorem, affine spaces.
This course presents a rigorous introduction to the elements of topology. Topics include a study of metric spaces, separation axioms, topological spaces, and topological properties of point sets and mappings.
This course is a first introduction to the ideas behind Algebraic Geometry: Nullstellensatz, the definition of varieties, and mappings between them. To Illustrate key ideas and motivate theorems, this course focuses its attention on concrete examples, often making use of mathematical software for visualization. Additionally, students will learn about computational techniques and how to use them. Starting with multi-variable calculus, this course will develop the theme of invariants attached to the geometry of curves and surfaces.
The various notations of curvature of surfaces are related to curvature and torsion of curves. The contrast between local and global phenomena is also emphasized. Visualization of ideas with mathematical software will be regularly present. This course is a continuation of MATH Topics include groups, rings, and fields, with applications to geometric constructability and solvability by radicals.
Math is now a level 2 course. This means that you can take it after taking Beginning Algebra rather than Intermediate Algebra. However, because of this change in prerequisites, be aware that this course may not transfer to schools other than the University of Wyoming or other Wyoming Community Colleges.
Math is not a valid course to prepare students for College Algebra. Contact Martin Stensing Martin. A good understanding of these concepts and their operations serves as a tool for understanding the other major concepts covered in this course: equations and inequalities.
After learning what equations and inequalities are, students spend the rest of the time learning how to manipulate and solve different types of equations and inequalities, including linear, quadratic, radical, rational and absolute value. The second part of college algebra, also known as intermediate algebra, focuses on graphing equations introduced in college algebra 1. Students learn how to find and graph the slope of a line, and how to write and graph equations of lines.
College algebra 2 also introduces students to some elementary topics in functions. In particular, students learn what a function is, how to do different operations of functions and how to graph certain functions. Graph linear equations. Express numbers in scientific notation. Addition, subtract, multiply, and divide polynomial expressions. Multiply and divide rational expressions. Calculate square roots, approximating those that are irrational.
Simplify square roots using the product and quotient rules. Equations and Inequalities in One Variable A. Solve literal equations that do not require factoring. Solve quadratic equations by factoring. Solve quadratic equations by using the square root property. Equations and Graphs in Two Variables A. Determine whether or not an equation is linear. Description: This course focuses on arithmetic and algebraic manipulation, equations and inequalities, graphs, and analysis of equations and graphs.
Objectives Factor algebraic expressions. Simplify arithmetic and algebraic expressions including those containing rational expressions, rational exponents, radicals, or complex numbers.
Use formulas and interpret results. Solve equations in one variable including quadratic, quadratic in form, and those containing rational expressions or radicals. Solve equations in more than one variable including systems of linear equations and literal equations. Graph quadratic functions and linear inequalities in two variables. Add and subtract rational expressions. Add, subtract, multiply, and divide complex numbers. Solve literal equations that require factoring.
Solve quadratic equations by completing the square. Solve quadratic equations by using the quadratic formula. Solve equations containing rational expressions. Solve equations containing radicals. Equations and graphs A. Identify the domain and range of a relation. Caveats: To successfully complete the pre-requisite s for this course, a student must earn at least a "C" in the prerequisite course s or earn an appropriate score on a placement exam.
Description: This course is an introductory approach to geometry. Objectives Classify geometric figures in two and three dimensions. Find the perimeter and area of two-dimensional geometric figures. Find the surface area and volume of three-dimensional figures. Write deductive proofs. Verify the congruence of geometric figures. Verify the similarity of geometric figures. Construct geometric figures with compass and straightedge. Geometric Shapes A. Define points, lines, and planes.
Define line segments, rays, and angles. Distinguish between different types of angles. Measure angles with a protractor. Define triangles and list their types. Define polygons and list their types. Define quadrilaterals and list their types. Compute the angle measures in a polygon. Identify prisms, pyramids, cylinders, cones, and spheres.
Identify regular polyhedra and list their types. Perimeter, Area, and Volume A. Compute the perimeter of a polygon. Compute the circumference of a circle. Compute the area of a regular polygon. Compute the area of a circle. Compute the length of a missing side in a right triangle. Reasoning A. Formulate conclusions. Apply conditional statements. Apply equivalent biconditional statements. Distinguish between valid and invalid deductions. Write a deductive proof. Triangles A.
Apply the triangle congruence theorems. Prove two triangles are congruent. Prove corresponding parts of congruent triangles are congruent. Define medians and perpendicular bisectors E.
Apply theorems related to isosceles and equilateral triangles. Apply theorems related to triangle inequalities. Parallel Lines and Quadrilaterals A. Apply theorems derived from the Parallel Postulate. Prove the Angle Sum in a Triangle Theorem. Apply the Exterior Angle Theorem. Prove theorems related to quadrilaterals. Similarity A. Solve problems related to ratio and proportion.
Compute the missing part of similar polygons. Apply theorems related to the geometric mean in a right triangle. Circles A. Define arc, central angle and inscribed angle. Compute measures of angles and arcs of a circle. Compute areas of sectors and measures of arc length. Define chords and tangents. Compute measures of segments and angles formed by chords. Prove theorems related to circles.
Constructions A. Construct segments and angles using a compass and straightedge. Construct perpendicular lines using a compass and straightedge. Construct parallel lines using a compass and straightedge. Subdivide line segments using a compass and straightedge. Construct the center of a circle using a compass and straightedge. Caveats: To successfully complete the pre-requisite s for this course, a student must earn at least a "C" in the pre-requisite course s or ea rn an appropriate score on a placement exam.
Description: This is a course for the student who needs specific skills in mathematics to address business problems and business applications. Objectives Solve percent problems. Apply mathematics to payroll situations. Apply mathematics to retail situations. Apply mathematics to finance situations. Apply mathematics to the valuation of assets. Use a financial calculator and a computer to apply mathematics to business problems. The Mathematics of Percents A.
Solve for base, rate, or part in a basic percent problem. Solve for the old or new value in a percent increase problem.
Solve for the old or new value in a percent decrease problem. The Mathematics of Payroll A. Given an hourly wage with an overtime policy, find the gross pay. Calculate FICA taxes.
Calculate federal and state unemployment taxes. Calculate the cost of employment to an employer. Use a computer to analyze the effect of taxes on gross pay.
The Mathematics of Retailing A. Analyze an invoice with key abbreviations. Calculate trade, series, and cash discounts. Calculate markup based on cost. Calculate markup based on selling price. Calculate markdowns. Calculate the adjusted cost when shrinkage is present. Calculate the net profit. Calculate operating loss and absolute loss. Calculate the amount of operating expenses from the percent. Calculate the break-even point. Find the interest earned using the simple interest formula.
Solve for principal, rate, or time in a simple interest problem. Determine the effective rate APR of a note. Calculate the present value of an annuity. The Valuation of Assets A. Description: This course is the first of a two-semester sequence that will introduce the mathematical skills and concepts necessary in technical work.
Objectives Simplify numerical and algebraic expressions. Solve linear equations and systems of linear equations. Solve problems using geometric properties and formulas. Manipulate formulas including those used in technical work. Construct truth tables by using Boolean algebra. Numeric Expressions A.
Describe the properties of the real number system. Simplify expressions involving exponents and radicals. Determine the number of significant digits in a number. Define ratio and proportion. Use conversion factors to convert various units of measure.
Measure using a ruler. Algebraic Expressions A. Add and subtract polynomials. Multiply polynomials. Divide polynomials. Evaluate algebraic expressions. Linear Equations A. Solve linear equations. Solve a proportion for a missing term. Solve a system of two or three equations by algebraic methods. Basic Geometry Skills A. Classify triangles. Calculate area and perimeter of polygons. Calculate area and circumference of circles. Calculate volume and surface area of geometric solids.
Graphing A. Plot points on the rectangular coordinate system. Graph straight lines. Define the slope of a line; use the slope to graph a line. Solve a system of equations by graphing. Logic A. Understand Venn diagrams. Construct truth tables. Evaluate using Boolean algebra. Description: This course is the second of a two-semester sequence on the mathematical skills and concepts necessary in technical work. Objectives Factor polynomials. Simplify and perform operations with rational expressions, radical expressions and complex numbers.
Solve quadratic, rational, radical, exponential and logarithmic equations. Use basic trigonometry. Algebraic Skills A.
Factor polynomials. Factor using greatest common factor. Factor using grouping. Factor trinomials. Factor using the difference of squares. Simplify rational and radical expressions. Convert between exponential and logarithmic notation. Equations A. Solve quadratic equations by factoring and by the quadratic formula. Solve problems involving direct, inverse and joint variation.
Solve equations involving rational expressions. Solve equations involving radical expressions. Solve exponential equations. Solve logarithmic equations. Trigonometry A. Define angle measurement in both radians and degrees. Evaluate trigonometric functions of any angle. Define inverse trigonometric functions. Solve right triangles for missing parts. Solve application problems using right triangle trigonometry. Define vectors. Perform operations with vectors. Graph transformations of the sine and cosine functions.
Description: This course will emphasize the beauty, scope, practical applications and relevance of mathematics. Objectives Apply set theory to practical applications. Determine the truth value of statements. Determine the validity of logical arguments. Use probability as a tool for predicting outcomes. Solve financial applications. Solve systems of equations and inequalities.
Solve linear programming applications. Calculate statistical measures of a data set. Set Theory A. Model set problems with Venn diagrams. Identify subsets. Logic and Deductive Reasoning A. Define conjunction, disjunction and negation of statements. Probability A. Determine whether or not two events are mutually exclusive. Calculate conditional probabilities.
Use counting formulas to determine permutations and combinations. Calculate mean, median, mode and standard deviation of a data set. Calculate expected value. Interpret statistical graphs.
Mathematics of Finance A. Calculate simple and compound interest. Calculate the value of an annuity. Calculate the annual percentage rate. Analyze an amortization schedule. Systems of Equations and Matrix Algebra A. Use linear functions to model applications. Solve systems of linear equations in two or more variables.
Identify the dimension of a matrix. Use Gaussian elimination to solve an augmented matrix. Linear Programming A. Graph systems of inequalities with all points of intersection. Solve a linear programming application graphically. Description: This course focuses on the study of functions and their graphs, techniques of solving equations, and applications.
Objectives Analyze functions and non-functions and their graphs. Sketch the graphs of circles and functions, including constant, linear, piecewise-defined, absolute value, square root, polynomial, rational, exponential and logarithmic.
Solve equations including polynomial, absolute value, radical, rational, exponential and logarithmic equations. Solve systems of equations and systems of linear inequalities. Solve inequalities including absolute value, polynomial and rational inequalities.
Create mathematical models to solve application problems and make predictions. Use function notation. Recognize equations of functions and non-functions. Determine the domain and range of a function. Construct an equation of a circle in standard form using: 1.
The center and radius. The endpoints of the diameter. The method of completing the square. Use graphs of functions for analysis. Find combinations and composites of functions. Find inverses of functions. Solutions of equations and inequalities A. Solve polynomial equations. Solve polynomial, absolute value and rational inequalities. Solve systems of linear inequalities by graphing. Applications to Real-World Situations A. Description: This is a course in trigonometric functions and graphs.
Objectives Define trigonometric functions for angles in standard position, in right triangles, and using the unit circle. Analyze the graphs of trigonometric, inverse trigonometric, and polar functions. Verify trigonometric identities. Solve trigonometric equations. Solve right and oblique triangles using trigonometric formulas.
0コメント