MATH D004 - Intermediate Algebra with PreAlgebra

• Students will be able to add and multiply complex numbers.
• Students will be able to add, multiply, and factor polynomials.
• Students will be able to add, multiply, divide, and simplify rational expressions.
• Students will be able to apply algebraic operations in the context of problem solving.
• Students will be able to evaluate formulas using algebraic substitution.
• Students will be able to graph linear and other functions.
• Students will be able to manipulate rational exponents and radicals in functions and equations.
• Students will be able to perform operations on real numbers.
• Students will be able to simplify algebraic and rational expressions.
• Students will be able to solve equations and inequalities with absolute values.
• Students will be able to solve linear equations and inequalities.
• Students will be able to solve linear systems of equations with 2 and 3 variables.
• Students will be able to solve quadratic equations using the quadratic formula, including all cases.
• Students will be able to effectively use basic arithmetical operations, fractions, and decimals.

MATH D005 - Intermediate Algebra

MATH D005 - Intermediate Algebra

• Students will be able to add and multiply complex numbers.
• Students will be able to add, multiply, and factor polynomials.
• Students will be able to add, multiply, divide, and simplify rational expressions.
• Students will be able to apply algebraic operations in the context of problem solving.
• Students will be able to evaluate formulas using algebraic substitutions.
• Students will be able to graph linear and other functions.
• Students will be able to manipulate rational exponents and radicals in functions and equations.
• Students will be able to simplify algebraic and exponential expressions.
• Students will be able to Solve equations and inequalities with absolute values.
• Students will be able to solve linear equations and inequalities.
• Students will be able to solve linear systems of equations with 2 and 3 variables.
• SStudents will be able to solve quadratic equations using the quadratic formula, including all cases.

MATH D200X - College Algebra Essentials

MATH D300 - Peer-Led Team Learning Laboratory for Pre-Calculus

• Students can pass Pre-Calculus.

MATH D301 - Peer-Led Team Learning Laboratory for Calculus I

• Students can pass Calculus I.

MATH 1060 - Quantitative Reasoning

• Students will be able to solve real-world problems requiring the use and interpretation of ratios in a variety of contexts.
• Students will be able to solve real-world problems relating to rates of change, including growth and decay.
• Students will be able to distinguish between absolute and relative rates of change and describe the difference using models.
• Students will be able to compare and contrast statements which are proportional and those that are not.
• Students will be able to create and use tables, graphs, and equations to model real-world situations and identify the limitations in proposed models.
• Students will be able to model financial applications such as credit card debt, installment savings, loans, etc. and calculate taxes, mortgage payments, etc.
• Students will be able to create basic linear and exponential models for real-world problems.
• Students will be able to choose most appropriate model for a given situation and describe the limitations of the proposed model.
• Students will be able to critically evaluate statistics being presented in the media, journals, and other publications.
• Students will be able to critically evaluate sampling strategy, the impact of sample size, and any inferences made.
• Students will be able to summarize and interpret data sets and compare two or more data sets in the light of the information presented.
• Students will be able to create visual representations of real-world data sets and be able to describe their strengths and limitations.
• Students will be able to calculate probabilities and conditional probabilities in real-world settings, and use them to draw conclusions.
• Students will be able to communicate quantitative findings and results verbally and in writing.

MATH 1090 - Consumer Mathematics

• Students can use elementary business mathematics in a variety of applications.

MATH 1101 - Elementary Topics in Mathematics I

• Students will be able to justify and explain the meaning of concepts explored, and represent these concepts verbally, numerically, symbolically, and with concrete manipulatives.
• Students will be able to describe and understand the relationships between sets, counting, cardinality, and one-to-one correspondence.
• Students will be able to describe and understand the base-10 number system and its connection to place value.
• Students will be able to construct the sets of natural, whole, rational, and irrational numbers and understand their properties.
• Students will demonstrate proficiency with arithmetic operations on natural, whole, rational, and irrational numbers through standard and nonstandard algorithms.

MATH 1102 - Elementary Topics in Mathematics II

• Students will be able to justify and explain the meaning of key concepts, and represent these concepts verbally, numerically, symbolically, and with concrete manipulatives.
• Students will be able to explain fundamental ideas of number theory, including divisors, factors, primes, prime factorization, composite numbers, greatest common factor, and least common multiple.
• Students will be able to use and explain quantitative reasoning and relationships that include ratio, rate, direct proportion, inverse proportion, and the use of units in problem situations.
• Students will be able to demonstrate proficiency in solving linear equations through both inverse operations and through alternative methods such as diagrams, and explain the relationships between these methods.
• Students will be able to use and convert between metric and U.S. customary units of measure of length, area, volume, weight, mass, and capacity, including choosing appropriate units for measurement, and describing the relationships between them.
• Students will be able to use and describe geometric measure in linear units, measures of area, surface area, volume, and additivity and invariance related to measurements.
• Students will be able to describe and use basic geometric objects in one, two, and three dimensions, such as line segments, lines, rays, angles, circles, arcs, polygons, polyhedral solids, cylinders, cones, and spheres.
• Students will be able to decompose 2D and 3D geometric objects into parts (e.g., a parallelogram into 2 triangles) and explain and justify properties of geometric objects.
• Students will be able to derive and explain the rationale behind formulas for perimeter, area, surface area, and volume of these two and three-dimensional figures.
• Students will be able to use and describe a variety of transformations & their properties (translations, rotations, reflections, glide reflections, dilations, compositions) and will express symmetry, congruence, and regularity in terms of transformations.

MATH 1200 - College Algebra

• Students will be able to analyze the algebraic structure and graph of functions to determine intercepts, domain, range, intervals on which the function is increasing, decreasing or constant, etc.
• Students will be able to determine algebraically and graphically whether the graph of an equation exhibits symmetry.
• Studens will be able to determine whether an algebraic relation or given graph represents a function.
• Students will be able to find inverses of functions and understand the relationship of the graph of a function to that of its inverse.
• Students will be able to perform operations with functions including addition, subtraction, multiplication, division and composition.
• Students will be able to perform transformations of functions including translations, reflections and stretching and shrinking.
• Students will be able to represent functions verbally, numerically, graphically and algebraically, including linear, quadratic, polynomial, rational, root/radical/power, exponential, logarithmic and piecewise-defined functions.
• Students will be able to solve a system of linear equations graphically and algebraically by substitution and elimination, and solve application problems that involve systems of linear equations.
• Students will be able to solve a variety of equations, including polynomial, rational, exponential, and logarithmic, including equations arising in application problems.
• Students will be able to solve polynomial and rational inequalities graphically and algebraically.
• Students will be able to understand the difference between an algebraic equation of one, two or more variables and a function and the relationship among the solutions of an equation in one variable, the zeros and intercepts of the corresponding function.
• Students will be able to use functions, including those listed in the first outcome, to model a variety of real-world problemsolving applications.
• Students will be able to use the Remainder and Factor Theorems for polynomial functions.

MATH 1200L - College Algebra Essentials

• Students will be able to use algebra concepts that are essential for College Algebra and apply to solve problems.
• Students will be able to use basic algebra skills to perform operations with functions.
• Students will be able to use factoring and other algebra concepts to solve polynomial and rational equations as well as inequalities.
• Students will be able to use algebra concepts to solve applied problems.

MATH 1250 - Introductory Game Theory

• Calculate Nash Equilibria in non-zero-sum games and identify stability and Pareto optimality of solutions.
• Calculate outcomes and find winning strategies in simple combinatorial games.
• Find dominance, saddle-points and mixed strategies for zero-sum and interpret their meanings in applications.
• Model games by game trees and calculate expected payoffs for branches.
• Model two entity conflicts, both zero- and non-zero-sum, as matrix games.
• Recognize game theory as a mathematical tool that is applicable in a large variety of contexts.
• Understand that non-linear problems can have surprising consequences, such as random winning strategies, existence of multiple solutions, and non-existence of acceptable solutions.
• Use linear equations, quadratic equations, and their graphs.
• Use the basic axioms and methods of discrete probability.
• Verify/disprove the axioms of utility and fairness in matrix games.

MATH 1260 - Finite Mathematics

• Students can recognize optimization problems and use linear programming as a tool to find solutions.
• Students can use elementary finite probabilities and expectation values in application problems.
• Students can use linear equations to model and solve application problems.
• Students can use the techniques of intermediate algebra in a variety of contexts.
• Students can use vector and matrix notations.

MATH 1300 - Pre-Calculus

• Analyze the algebraic structure and graph of a function to determine intercepts, domain, range, intervals on which the function is increasing, decreasing or constant, etc.
• Define the six trigonometric functions in terms of right triangles and the unit circle.
• Determine algebraically and graphically whether the graph of an equation exhibits symmetry.
• Determine whether an algebraic relation or given graph represents a function.
• Express angles in both degree and radian measure.
• Find inverses of functions and understand the relationship of the graph of a function to that of its inverse.
• Identify and express the conics (quadratic equations in two variables) in standard rectangular form, graph the conics, and solve applied problems involving conics.
• Identify and express the general term of arithmetic and geometric sequences, and find the sum of arithmetic and geometric series.
• Perform basic vector operations both graphically and algebraically addition, subtraction, and scalar multiplication.
• Perform operations with functions addition, subtraction, multiplication, division, and composition.
• Perform transformations of functions translations, reflections and stretching, and shrinking.
• Represent functions verbally, numerically, graphically and algebraically, including linear, quadratic, polynomial, rational, root/radical/power, piecewise-defined, exponential, logarithmic, trigonometric, and inverse trigonometric functions.
• Represent sequences verbally, numerically, graphically and algebraically, including both the general term and recursively.
• Represent vectors graphically in both rectangular and polar coordinates and understand the conceptual and notational difference between a vector and a point in the plane.
• Solve a system of linear equations graphically and algebraically by substitution and elimination, and solve application problems that involve systems of linear equations.
• Solve a variety of equations, including polynomial, rational, exponential, and logarithmic, trigonometric and inverse trigonometric, including equations arising in application problems.
• Solve a variety of trigonometric and inverse trigonometric equations, including those requiring the use of the fundamental trigonometric identities, in degrees and radians for both special and non-special angles.
• Solve application problems that involve trigonometric equations.
• Solve application problems using vectors.
• Solve polynomial and rational inequalities graphically and algebraically.
• Solve right and oblique triangles in degrees and radians for both special and non-special angles, and solve application problems that involve right and oblique triangles.
• Understand the difference between an algebraic equation of one, two or more variables and a function, and the relationship among the solutions of an equation in one variable and features of the graph.
• Use functions, including those listed in the first outcome, to model a variety of real-world problem solving applications.
• Use the Remainder and Factor Theorems for polynomial functions.
• Verify trigonometric identities by algebraically manipulating trigonometric expressions using fundamental trigonometric identities, including the Pythagorean, sum and difference of angles, double-angle, and half-angle identities.
• Write series in summation notation, and represent sequences of partial sums verbally, numerically, and graphically.

MATH 1321 - Elementary Applied Mathematics I

• Students will be able to analyze the algebraic structure and graph of functions to determine intercepts, domain, range, aymptotes, where the function has symmetry (even/odd), etc.
• Students will be able to analyze functions and their graphs to determine intervals on which the function is increasing, decreasing or constant, the vertex of a quadratic function.
• Students will be able to determine algebraically and graphically whether the graph of an equation exhibits symmetry.
• Students will be able to determine whether an algebraic relation or given graph define a function.
• Students will be able to find inverses of functions listed in the first outcome and understand the relationship of the graph of a function to that of its inverse. Students will use the Remainder and Factor Theorems for polynomial functions.
• Students will be able to identify and express the general term of arithmetic and geometric sequences, and find the sum of arithmetic and geometric series.
• Students will be able to perform transformations of functions including translations, reflections and stretching and shrinking. Perform operations with functions: addition, subtraction, multiplication, division and composition.
• Students will be able to represent functions verbally, numerically, graphically & algebraically, including polynomial, rational, root/radical/power, piecewise-defined, exponential, and logarithmic functions.
• Students will be able to apply knowledge of sequences/series to represent sequences verbally, numerically, graphically and algebraically, including both the general term and recursively.
• Students will be able to solve a system of linear equations graphically and algebraically by substitution and elimination, & solve application problems that involve systems of linear equations.
• Students will be able to solve polynomial and rational inequalities graphically and algebraically.
• Students will be able to solve a variety of equations, including polynomial, rational, exponential, and logarithmic, including equations arising in application problems.
• Students will be able to understand the average rate of change of the graph of a function or equation on an interval.
• Students will be able to understand the difference between an algebraic equation and a function, and the relationship among the solutions of an equation in one variable, the zeros of the corresponding function, and the coordinates of the x-intercept.
• Students will be able to use functions to model a variety of real-world problem solving applications.
• Students will be able to write series in summation notation, and represent sequences of partial sums verbally, numerically and graphically.

MATH 1322 - Elementary Applied Mathematics II

• Analyze the algebraic structure and graph of trigonometric and inverse trigonometric functions to determine whether the function is one-one, exhibits any symmetry (even/odd), etc.
• Analyze the algebraic structure and graph of trigonometric and inverse trigonometric functions to determine intercepts, domain, range, intervals on which the function is increasing, decreasing or constant, asymptotes,
• Angles/Triangles. Express angles in both degree and radian measure.
• Convert points and equations between rectangular and polar form.
• Identify and express the conics (quadratic equations in two variables) in standard rectangular form, graph the conics, and solve applied problems involving conics.
• Perform basic vector operations both graphically and algebraically addition, subtraction, and scalar multiplication.
• Perform transformations of trigonometric and inverse trigonometric functions translations, reflections and stretching and shrinking (amplitude, period and phase shift).
• Represent trigonometric and inverse trigonometric functions verbally, numerically, graphically and algebraically; define the six trigonometric functions in terms of right triangles and the unit circle.
• Represent vectors graphically in both rectangular and polar coordinates and understand the conceptual and notational difference between a vector and a point in the plane.
• Solve a variety of trigonometric and inverse trigonometric equations, including those requiring the use of the fundamental trigonometric identities, in degrees and radians for both special and non-special angles.
• Solve application problems that involve trignometric equations.
• Solve application problems using vectors.
• Solve right and oblique triangles in degrees and radians for both special and non-special angles, and solve application problems that involve right and oblique triangles.
• Use trigonometric and inverse trigonometric functions to model a variety of real-world problem-solving applications.
• Verify trigonometric identities by algebraically manipulating trigonometric expressions using fundamental trigonometric identities, including the Pythagorean, sum and difference of angles, double-angle and half-angle identities.

MATH 1350 - Survey of Calculus

• Apply differential calculus to business applications.
• Apply integral calculus to business applications.
• Demonstrate the ability to determine indefnite integrals, use the Fundamental Theorem of Calculus, and integrate by substitution and by parts.
• Determine derivatives of Exponential and Logarithmic Functions.
• Determine derivatives using the power rule, sum & difference rules, product rule, quotient rule, and chain rule.
• Determine higher order derivatives of a function. Understand velocity as the derivative of position and acceleration as the 2nd derivative of position.
• Determine the absolute extrema of a continuous function on a closed interval.
• Determine the continuity of functions at a point or on intervals.
• Determine the limits of functions graphically, numerically, and analytically. Recognize and determine infinite limits and limits at infinity.
• Understand the business terminology of demand, cost, price, revenue, and profit. Use linear, polynomial, rational, algebraic, exponentail, and logarithmic functions in business applications.
• Understand the business terminology of marginal quantities, including marginal cost, marginal revenue, and marginal profit.
• Understand the interpretation of the derivative as the slope of a line tangent to a graph and as the rate of change of a dependent variable with respect to an independent variable and determine the derivative of a function using the limit definition.
• Use and solve differential equations to model growth and decay.
• Use defnite integrals in applications such as determining the area of an enclosed region and fnding the average value of a function.
• Use differentials in approximation problems.
• Use the first and second derivatives to analyze and sketch the graph of a function, including determining intervals on which the graph is increasing, decreasing, constant, concave up, concave down, and finding relative extrema and inflection points.

MATH 1500 - Introductory Statistics

• Students will be able to summarize univariate and bivariate data, quantitative and qualitative data by employing appropriate graphical, tabular, and numerical methods and interpret the information from these graphs.
• Students will be able to describe the attributes of the data or the relationships between the data and distinguish between quantitative and qualitative datasets, univariate and bivariate datasets.
• Students will be able to identify the characteristics of a well-defined study and critically evaluate various aspects of the study, recognize the limitations of the study and also recognize common sources of bias in surveys.
• Students will be able to compute and interpret various measures of central tendency (mean, median, partition values, etc.) and variation (standard deviation, variance, etc.).
• Students will be able to compute and interpret correlation coefficient and regression lines from a given bivariate dataset.
• Students will be able to model random phenomenon and assign probabilities, compute probabilities, and conditional probabilities.
• Students will be able to obtain and describe probability distributions, compute expected gain/loss, and make inferences based on these computations.
• Students will be able to compute probabilities using normal distributions.
• Students will be able to identify the statistic and the parameter in a research problem, explain the difference between them, and describe the sampling distribution.
• Students will be able to construct confidence intervals for mean and proportion, compute and interpret margin of error, compute sample size for a given margin of error, and determine the effect of changing the sample size or confidence level.
• Students will be able to formulate null and alternative hypotheses in the case of research problems involving mean and proportions, test the significance of null and alternative hypotheses using critical and p-values and interpret the results.
• Students will be able to use appropriate technology such as spreadsheets or statistical software to perform statistical computations.
• Students will be able to interpret statistical results and information in news stories and journal articles and apply the concepts learned in the course to their discipline of study or a related area.

MATH 2110 - Introductory Geometry for Middle School Teachers

• (NCATE-11) Candidates use spatial visualization and geometric modeling to explore and analyze geometric shapes, structures, and their properties, including:
• 11.1 Demonstrate knowledge of core concepts and principles of Euclidean geometry in two and three dimensions.
• 11.2 Exhibit knowledge of informal proof.
• 11.3 Build and manipulate representations of two- and three-dimensional objects and perceive an object from different perspectives.
• 11.4 Specify locations and describe spatial relationships using coordinate geometry.
• 11.5 Analyze properties and relationships of geometric shapes and structures.
• 11.6 Apply transformation and use congruence, similarity, and line or rotational symmetry.

MATH 2120X - Number and Algebra for Middle School Teachers

MATH 2301 - Calculus I

• Students can use the tools of differential and integral calculus in a variety of applications.

MATH 2301A - Honors Experience: Calculus I

MATH 2302 - Calculus II

• Students can use the tools of differential and integral calculus in a variety of applications.

MATH 2302A - Honors Experience: Calculus II

MATH 2500 - Statistics and Probability

• Students will be able to select and produce appropriate graphical, tabular, and numerical methods to summarize qualitative and quantitative data, univariate and bivariate data, and interpret and summarize the information into verbal descriptions.
• Students will be able to identify the characteristics of a well-defined study and critically evaluate various aspects of the study, recognize the limitations of the study and also recognize common sources of bias in surveys.
• Students will be able to compute and interpret various measures of central tendency (mean, median, partition values, etc.) and dispersion (standard deviation, variance, etc.).
• Students will be able to investigate and describe the relationships or associations between two variables using caution in interpreting correlation and association, compute and interpret correlation coefficient and regression lines.
• Students will be able to construct and model a random phenomenon using outcomes, events, and the assignment of probabilities, use addition and multiplication probability rules, and also compute conditional probabilities.
• Students will be able to obtain and describe probability distributions, differentiate between discrete and continuous distributions, compute expected gain/loss, and make inferences based on these computations.
• Students will be able to compute probabilities using theoretical probability distributions (binomial, normal, etc.) and interpret z-scores.
• Students will be able to obtain and describe sampling distributions of mean, proportion, difference of means, difference of proportions, etc. and use the Central Limit Theorem.
• Students will be able to estimate parameters, construct confidence intervals, compute and interpret margin of error, compute sample size for a given margin of error, and determine the effect of changing the sample size or confidence level.
• Students will be able to formulate null and alternative hypotheses for a given research problem and describe the logic and framework of the inference of hypothesis testing.
• Students will be able to perform a hypothesis test for a mean, proportion, difference of means, difference of proportions, etc. for large and small samples using p-value and critical (z and t) values and interpret statistical and practical significance.
• Students will be able to perform chi-square test for hypotheses testing, analyze the results, and interpret these results.
• Students will be able to use appropriate technology to carry out descriptive and inferential analysis of data and to perform statistical computations.

MATH 2500A - Honors Experience in Introduction to Statistics

MATH 2530X - Foundations of Data Science

MATH 2900 - Special Topics in Mathematics

• Students will increase their knowledge in Mathematics.

MATH 2970T - Mathematics Tutorial

• HTC students should be able to work effectively with difficult, multi-dimensional subjects be they inside or outside a student’s primary area of study.

MATH 2971T - Mathematics Tutorial

• HTC students should be able to work effectively with difficult, multi-dimensional subjects be they inside or outside a student’s primary area of study.

MATH 2980T - Mathematics Tutorial

• HTC students should be able to work effectively with difficult, multi-dimensional subjects be they inside or outside a student’s primary area of study.

MATH 2981T - Mathematics Tutorial

• HTC students should be able to work effectively with difficult, multi-dimensional subjects be they inside or outside a student’s primary area of study.

MATH 3000 - History of Mathematics

• Students should develop an understanding of instructional strategies that enhance student learning.
• Students will be able to apply historical methods to mathematical histories and to critically analyze mathematical histories.
• Students will demonstrate working knowledge of key moments and figures in mathematics history.
• Students will see the development of mathematics beyond western mathematics and will understand the nature of mathematics as process and discipline.
• Students will understand the role of histories of mathematics in their chosen field.

MATH 3050 - Discrete Mathematics

• Able to apply induction for proving properties of discrete structures.
• Able to count or enumerate objects, perform combinatorial analysis to solve counting problems.
• Able to use discrete structures in application areas like computer science, optimization, probability.
• Able to use set notation and logical statements correctly in the above contexts.
• Able to use standard proof methods in the context of simple problems in elementary number theory.
• Understands the mathematics of graphs and trees, and how to use graphs as models in a variety of areas.

MATH 3060 - Introduction to Mathematical Reasoning, Problem Solving, and Proof

• Students will be able to analyze hypotheses, constraints, connections, and conclusions in mathematical statements.
• Students will be able to formulate and test conjectures and generalizations.
• Students will be able to write, speak, analyze, and critique arguments and proofs.
• Students will be able to construct proofs using logic, definitions, and theorems and write them systematically.
• Students will be able to construct valid arguments, proofs, refutations, counterexamples, definitions, theorems, axioms, examples, and nonexamples.
• Students will be able to identify examples, nonexamples, invalid and valid arguments and proofs.
• Students will be able to analyze the role, value, necessity, and nature of proof.

MATH 3060X - Introduction to Mathematical Reasoning, Problem Solving, and Proof

MATH 3070 - Introduction to Number Theory

• Students can construct proofs of fundamental results in number theory.
• Students understand how number theory is important in modern applications.

MATH 3110 - College Geometry

• Demonstrate the dependence of some of the axioms commonly included in axiom sets for high school math books.
• Demonstrate the independence of the Parallel Postulate using examples from Euclidean and Hyperbolic Geometry.
• Incorporate methods of similarity, transformations, coordinates, vectors, matrices, complex numbers, and symmetry to simplify proofs or solve geometric problems.
• Prove a core batch of the standard theorems of Neutral, Euclidean, and Hyperbolic Geometry using deductive, axiom-based proofs.
• Solve geometric problems using the axioms and theorems of Euclidean Geometry.
• Use computer programs to produce dynamic drawings to illustrate geometric theorems and problems.

MATH 3200 - Applied Linear Algebra

• Students can competently carry out computations involving solutions of linear systems of equations and eigenvalues.
• Students can effectively manipulate matrix equations.
• Students understand and can use the geometry of linear systems and matrices.

MATH 3200A - Honors Experience in Applied Linear Algebra

MATH 3210 - Linear Algebra

• Students can competently carry out computations involving solutions of linear systems of equations and eigenvalues.
• Students can effectively manipulate matrix equations.
• Students can prove basic results of linear algebra.
• Students understand and can use the geometry of linear systems and matrices.

MATH 3240 - Abstract Algebra

• Students can prove elementary results about algebraic structures.
• Students will develop awareness and appreciation of the axiomatic method as well as familiarity with basic algebraic structures.

MATH 3300 - Calculus III

• Students can use the tools of differential and integral calculus in higher dimensions.

MATH 3320 - Vector Analysis

• Students will understand and be able to compute differential and integral quantities involving vectors.

MATH 3400 - Elementary Differential Equations

• Students can find analytic solutions of a variety of linear differential equations.
• Students understand the meaning of differential equations as models and the meaning of a solution.

MATH 3400A - Honors Experience: Elementary Differential Equations

MATH 3500 - Probability

• Calculate probabilities using various methods.
• Conduct simple mathematical proofs in a rigorous manner.
• Derive important characteristics (mean, variance, MGF) for frequently used distributions.
• Find confidence intervals and conduct simple hypotheses tests for univariate case.

MATH 3505X - Applied Linear Models

MATH 3560 - Theory of Interest

• Students will be able to perform calculations relating to present value, current value and accumulated value.
• Students will be able to calculate present value, current value and accumulated value for sequences of non-contingent payments.
• Students will be able to perform calculations connected with bonds.
• Students will be able to perform calculations relating to loans.
• Students will be able to perform calculations associated with yield curves, rates of return, measures of duration and convexity.
• Students will be able to perform calculations related to cash flow matching and immunization.
• Students will be able to perform calculations associated with interest rate swaps.

MATH 3560X - Theory of Interest

MATH 3600 - Applied Numerical Methods

• Define and understand the practical consequenses of issues such as convergence, stability, computational cost, and error propagation as they apply to various numerical problems.
• The ability to use MATLAB as a programming tool to solve common engineering and scientific problems.
• Understand and know how to apply commonly used numerical methods for solving equations and linear systems, integration and differential equations.

MATH 3680 - Quantitative Foundations for Bioinformatics

• Ability to interpret the meaning of the output of these software tools in biological terms.
• Ability to recognize typical sources of uncertainty or outright invalid answers that occur in using these software tools.
• Ability to recognize which types of bioinformatics software will give solutions to the mathematical problems that correspond to given biological ones.
• Ability to translate certain types of biological data into mathematical ones.
• Ability to understand how parameter choices will affect the output.
• Familiarity with the most basic algorithms that are used by these software tools.

MATH 3970T - Mathematics Tutorial

• HTC students should be able to work effectively with difficult, multi-dimensional subjects be they inside or outside a student’s primary area of study.

MATH 3980T - Mathematics Tutorial

• HTC students should be able to work effectively with difficult, multi-dimensional subjects be they inside or outside a student’s primary area of study.

MATH 4100 - Teaching of Mathematics in Secondary School

• 1. Describe the significance, content, philosophy, and impact on reform of national and state standards (including achievement testing, the High School Graduation Test, and implications of CORE).
• 2. Describe credible theories of learning mathematics including constructivism and its variants.
• 3. Explain how research in mathematics education is conducted, reported, and applied to teaching and learning practices.
• 4. illustrate how to use technology (including graphing calculators, software, video, and the Internet while also identifying benefits and obstacles of technology to maximizing student learning (PPP1).
• 5. Give examples of questioning strategies for the classroom that promote mathematical thinking and dialogue (discourse).
• 6. Use multiple strategies to support mathematics instruction including differentiation to meet the needs of all learners.
• 7. Recognize the essential parts of a lesson plan and prepare a lesson plan that includes outcomes, materials, structured sequence of experiences for students, a logical closure, a planned extension, and a plan for assessment.
• 8. Describe a variety of strategies that teachers can use to promote positive classroom management and the role that effective lesson planning has on classroom environment.
• 9. Use a variety of assessment strategies to collect data, including electronic means, regarding student academic progress and dispositional development, and to communicate assessment items to student as productive feedback.
• 10. Participate in programs for professional growth in mathematics education including NCTM, OCTM, OUCTM, journals, ORC, and understand the need for continuous professional improvement.
• 11. Describe (and demonstrate in lesson planning) how to make the five mathematical processes -such as problem solving, reasoning and proof, communication, connections, and representation - the focus of an AYA mathematics program.
• 12. Criteria for assessing the appropriateness of various technologies will be a focus of this objective (PPP2).
• 13. Identify, select, and use hardware and software technology resources to meet specific teaching and learning objectives (PPP4).
• 14. Write instructional objectives at the knowledge/skill, conceptual, and application levels.
• 15. Recognize the use of technology-enriched learning activities in the classroom and write lesson plans that make use of technology to address diverse student needs, as appropriate and available (PPP7, 17, 22).
• 16. Recognize that each student has individual needs and illustrate how a variety of teaching approaches, including the use of manipulatives and the use of technology, can be used to appeal to the learning style of each student (PPP1, 3, 6).
• 17. Exhibit facility with resources to gather field-tested ideas for use in one’s own classroom, including electronic resources (PPP10).
• 18. Grow in his/her appreciation of the role of mathematics in the AYA curriculum.
• 19. Continue to develop a positive disposition toward the field of mathematics.
• 20. Understand the role of community, place, and parents in mathematics education.
• Throughout the course, lectures, readings, written assignments, collaborative engagements, and popular cultural resources will help students achieve these outcomes. In particular, students will..

MATH 4100L - Teaching of Mathematics in Secondary School Early Field Experience

• Same as MATH 4100 Teaching Mathematics in Secondary Schools.

MATH 4150 - Advanced Perspectives for Math Teachers

• After completion of the course, the student will be able to contextualize the mathematics content learned for their program in the content they will teach at the high school level.
• Analyze common mathematical problems and real-world models using functions.
• Analyze solutions of mathematical problems to determine alternative means of solving and/or representing the solution, and ways of extending and/or generalizing the problem.
• Analyze the origins, representations, and applications of mathematical concepts.
• Apply and prove the Division Algorithm and Euclidean Algorithm.
• Construct and analyze proofs using mathematical inductions.
• Describe the various ways of representing and defining of functions.
• Develop and apply algebraic properties of modular arithmetic systems.
• Explain the construction of the real and complex number systems and various ways of representing real and complex numbers.
• Extend the Division and Euclidean Algorithm to polynomials.
• In particular, the student will be able to perform, analyze, and see the connections between the following skills and concepts and to the application of these skills to high school mathematics instruction. The skills/processes include:
• Recognize and prove various logical equivalences to mathematical induction.
• Relate integer congruence to real-world applications. Prove and apply the Chinese Remainder Theorem.
• Relate properties of the real and complex number systems to general ordered fields.
• Use the theory of functions in solving equations and inequalities.

MATH 4221 - Modern Algebra I

• Students will enhance their understanding and appreciation of the axiomatic method as well as their familiarity with basic algebraic structures and their ability to write proofs.

MATH 4222 - Modern Algebra II

• Students will enhance their understanding and appreciation of the axiomatic method as well as their familiarity with basic algebraic structures and their ability to write proofs.

MATH 4230 - Introduction to Algebraic Coding Theory

• Students will learn about this important application of Modern Algebra.
• They will understand the criteria for goodness of the various error-correcting codes studied and will be able to do the appropriate calculations to design the codes and to use them to correct a prescribed number of errors.

MATH 4301 - Advanced Calculus I

• Students are prepared for graduate study and research in mathematics.
• Students can understand and can prove the foundations of calculus.

MATH 4302 - Advanced Calculus II

• Students are prepared for graduate study and research in mathematics.
• Students can prove and use fundamental theorems about the convergence of functions.

MATH 4310 - Complex Variables

• Students can prove basic theorems about analytic functions.
• Students can use complex variables as tool for applications.

MATH 4330 - Hilbert Spaces and Applications

• Can prove basic properties of Hilbert spaces and other functions spaces.
• Can use Hilbert space techniques in applications.
• Students will understand the concepts and properties of function spaces and their properties.

MATH 4400 - Advanced Differential Equations

• Students will have a good understanding of linear systems of ordinary differential equations.

MATH 4410 - Fourier Analysis and Partial Differential Equations

• Ability to use the separation of variables method in the study of classical equations of mathematical physics.

MATH 4470 - Applied Dynamical Systems

• Students will have tools for the analysis of dynamical systems that arrise in applications.
• Students will understand the basic concepts of dynamical systems and how they are used.
• Students will understand the role of dynamical systems as models for applications.

MATH 4500 - Theory of Statistics

• Analyze and compare different point estimators.
• Compute various probabilities and expectations by various methods.
• Conduct various standard hypotheses tests, compute the power functions, find the UMP test using Neyman-Pearson Lemma, and find the likelihood-ratio test.
• Find a confidence interval for a parameter for various distributions.
• Find a point estimator of a parameter using various methods.
• Find distributions of functions of random variables.

MATH 4510 - Applied Statistics

• Analyze simple linear regression models; derive point estimators, confidence intervals, and test statistics.
• Apply the ANOVA model to the experimental design data.
• Use nonparametric method for hypotheses tests when the underlying conditions for parametric tests are violated.

MATH 4520 - Stochastic Processes

• Analyze Poisson process and its generalizations.
• Analyze simple renewal processes and queuing models.
• Understand and analyze important MC models.
• Use conditioning techniques to find probabilities and expectations.

MATH 4530 - Statistical Computing

• Conduct data analysis using one or more major statistical models.
• Generate distributions by various methods.
• Use computer-intensive method for estimation and hypotheses testing.

MATH 4550 - Basic Principles of Actuarial Science

• Be equipped with basic skills required for the first actuarial science exam.
• Find probabilities, moments, and distributions using various methods.
• Solve the problems arising in the context of risk management.

MATH 4560 - Life Contingencies

• Students will be able to work with key concepts concerning parametric and non-parametric models including single life, multiple life and multiple decrements.
• Students will be able to perform calculations on present value random variables associated with benefits and expenses for different survival models.
• Students will be able to calculate and interpret probabilities, means, variances and percentiles for the present value random variable.
• Students will be able to calculate the effect of changes in underlying assumptions such as mortality and interest on the present value random variable.
• Students will be able to use and explain premium calculation methodologies.
• Students will be able to calculate and interpret probabilities, means, variances and percentiles of random variables associated with premiums.
• Students will be able to calculate premiums based on the equivalence principle, the portfolio percentile premium principle and profit testing.
• Students will be able to calculate and interpret probabilities, means, variances and percentiles for random variables associated with reserves.
• Students will understand premium reserves for insurances and annuities for survival models and different premium types, including net premium, modified premium, gross premium and expense.
• Students will be able to calculate and interpret common profit measures such as expected profit, actual profit and break-even year.
• Students will be able to apply survival models, different types of premiums and reserves calculations to pension plans and retirement benefits.

MATH 4580X - Elements of Financial Mathematics

MATH 4600 - Introduction to Numerical Analysis

• Analyze the accuracy of such algorithms.
• Analyze the computational cost and efficiency of such algorithms.
• Construct algorithms to solve mathematical problems based on a common set of strategies.
• Identify the sources of failure of such algorithms, and avoid them.

MATH 4610 - Introduction to Waves and Wavelets with Applications

• Understanding mathematical theory about conservation and compaction of energy, multiresolution analysis, and the Fourier-wavelet connection.
• Developing ability to perform wavelet transform and discrete Fourier transform using computer software and basic wavelet-based problem solving techniques.
• Expanding knowledge about related numerical algorithms and their implementation.

MATH 4620 - Linear and Nonlinear Optimization

• Students will know how to formulate real-life problems as linear and nonlinear programs, apply algorithms to solve the problems, and understand the theory behind the solution methods which will help them to analyze the algorithms and design new ones.

MATH 4630 - Discrete Modeling and Optimization

• Students will know how to build optimization models using binary integer variables, dynamic programs, and mathematical networks;
• Analyze the algorithms in terms of their accuracy and efficiency.
• Apply algorithms to solve the optimization problems.
• Understand the theory behind the algorithms.

MATH 4700 - Introduction to Topology

• Distinguish between homeomorphic and non-homeomorphic subsets of Euclidean spaces.
• Formulate and prove generalizations of the Intermediate Value Theorem and the Extreme Value Theorem in the setting of metric spaces.
• Provide classification of compact 2-manifolds.
• Provide examples of convergent and divergent sequences in metric spaces.
• Recognize certain compact groups, such as groups of rotations of Euclidean spaces.

MATH 4900 - Special Topics in Mathematics

• Students will increase their knowledge in Mathematics.

MATH 4930 - Studies in Mathematics

• Student will gain expertise in a field of mathematics.

MATH 4940 - Mathematics Research

• Student will complete a research project in mathematics.
• The student will gain proficiency in written and oral communication of mathematics and its applications.

MATH 4970T - Mathematics Tutorial (thesis)

• To equip students to pursue independent research in mathematics.
• To provide students with a sophisticated understanding of mathematics.

MATH 4980T - Mathematics Tutorial (thesis)

• To equip students to pursue independent research.
• To provide students with a sophisticated understanding of their primary area of study.

MATH 4993 - Undergraduate Mathematics Seminar I

• Students will be able to integrate advanced topics in mathematics and its applications into a plan for individual study.
• Students will be able to develop an outline for a seminar in a chosen topic.

MATH 4994 - Undergraduate Mathematics Seminar II

• Students will be able to synthesize background material and an advanced topic of interest.
• Students will be able to effectively present mathematics and its applications orally.
• Students will able to appropriately utilize technology to acquire, organize and present mathematics.

ME 1010 - Mechanical Engineering - Gateway Course

• Students will be able to evaluate ethical issues that may occur in professional practice.
• Students will be able to use graphical techniques in problem formulation and solution.
• Students will be able to use mathematics, experimentation, and computation in solving problems.
• Students will be able to explain the influence of science and technology on civilizations and how science and technology have been applied to the betterment of humankind.
• Students will be able to discuss the engineering profession, the mechanical/energy engineering discipline, and an engineer’s role in society.
• Students will be able to identify the faculty, staff, and student organizations of the mechanical engineering department and energy engineering program at Ohio University.
• Students will be able to demonstrate fluency in both English and SI units and an ability to translate between them.
• Students will be able to discuss the role of engineering ethics in professional problem solving.
• Students will be able to demonstrate familiarity with the NSPE Code of Ethics and its use in professional decision making.

ME 1800 - Mechanical Engineering Colloquium I

• Students will be able to describe connections between the mechanical engineering program of study and the practice of engineering
• Students will be able to describe contemporary areas of research and development in mechanical engineering
• Students will be able to describe research and scholarly activities of the Mechanical Engineering faculty of the Russ College of Engineering and Technology

ME 2800 - Mechancial Engineering

• Students will be able to identify typical responsibilities for an engineer in their discipline.
• Students will be able to respond to interview questions related to personal effectiveness competencies.
• Students will be able to discuss aspects of and identify methods for improving their emotional intelligence.
• Student will be able to identify different methods for positive influence in multiple situations.
• Students will be able to identify and implement methods for more effective teamwork.
• Students will be able to discuss leadership characteristics and roles.

ME 2900 - Special Topics in Mechanical Engineering

• Students will be able to meet the outcomes of the course as established by the instructor.

ME 3011 - Kinematics and Dynamics of Machines

• Students will be able to identify common mechanisms used in machines and everyday life.
• Students will be able to calculate the mobility (number of degrees-of-freedom) of planar structures, mechanisms, and robots.
• Students will be able to perform complete translational and rotational mechanism position analysis.
• Students will be able to perform complete translational and rotational mechanism velocity analysis.
• Students will be able to perform complete translational and rotational mechanism acceleration analysis.
• Students will be able to perform complete translational and rotational mechanism inverse dynamics analysis via the matrix method.
• Students will be able to classify cam mechanisms, and design cam motion profiles.
• Students will be able to classify gear mechanisms and calculate gear motion and torque given the gear ratio.
• Students will be able to perform linearized dynamic modeling for vibrational systems

ME 3012 - Linear Systems Analysis and Control

• Students will be able to explain the history and some examples of control systems.
• Students will be able to accomplish linear system modeling.
• Students will be able to solve linear initial value problem ordinary differential equations.
• Students will be able to use Laplace transforms for linear initial value problem ordinary differential equations solutions and control systems derivations.
• Students will be able to derive transfer functions and draw block diagrams.
• Students will be able to analyze the stability, disturbances, transient and steady-state responses, dynamic shaping of responses for feedback control systems.
• Students will be able to design and simulate linear single-input, single output controllers for dynamic systems via parameter matching.
• Students will be able to design output attenuation correction factors, plus internal and external pre-filters for control systems.
• Students will be able to apply the root-locus method for the design and analysis of feedback control systems.
• Students will be able to solve first- and second-order, free and forced, undamped and damped mechanical vibrational systems initial value problem ordinary differential equations.

ME 3022 - Heat and Fluid Transport I

• Students will be able to explain key fluid mechanics concepts including viscosity, surface tension, and turbulence.
• Students will be able to calculate hydrostatic and buoyant forces on submerged shapes.
• Students will be able to construct and solve Bernoulli’s equation for engineering applications.
• Students will be able to analyze internal flow in pipes.
• Students will be able to apply Buckingham Pi Theorem, dimensional analysis, and scaling.

ME 3122 - Heat and Fluid Transport II

• Students will be able to identify and explain different heat transfer modes in engineering systems.
• Students will be able to identify and explain thermal properties of solids.
• Students will be able to identify and explain thermal boundary layers in fluids.
• Students will be able to identify and explain black-body and real-surface radiation exchange.
• Students will be able to solve for heat flow rate and/or temperature profile in problems with one dimensional steady state heat transfer with no heat generation.
• Students will be able to solve for heat flow rate and/or temperature profile in problems with one dimensional transient heat transfer with no spatial effects.
• Students will be able to solve for heat flow rate and/or temperature profile in problems with convective heat transfer during flow over a flat plate.
• Students will be able to solve for heat flow rate and/or temperature profile in problems with convective heat transfer during flow through channels.
• Students will be able to solve for heat flow rate and/or temperature profile in problems with radiative heat transfer at a surface.
• Students will be able to solve for heat flow rate and/or temperature profile in problems with radiative energy exchange between two surfaces.

ME 3140 - Introduction to Manufacturing Processes

• Students will be able to identify basic manufacturing processes and ascertain the types of products that are cost effectively produced with these processes.
• Students will be able to analyze manufacturing processes using engineering principles to determine basic operating parameters.
• Students will be able to apply statistical techniques to manufacturing, including statistical process control (SPC) and the computation of process capability/performance.
• Students will be able to characterize major metal alloy systems and their physical characteristics with respect to design requirements and manufacturing processes.
• Students will be able to apply metal heat treating principles (quenching and tempering, solutionizing and aging, and annealing operations), and assess the effect on mechanical properties
• Students will be able to perform energy calculations related to manufacturing processes.
• Students will be able perform metal forming analyses and load calculations using fundamental principles.

ME 3510 - Computer Aided Design

• Students will be able to create fully constrained solid models that can be quickly modified using standard software tools.
• Students will be able to use finite element analysis software to mesh a solid model, apply meaningful loads and boundary conditions, complete a linear static stress analysis, and interpret the results.
• Students will be able to use standard software tools to create engineering drawings, or other documents, to fully describe the geometries and dimensions of parts, as well as to document assemblies according to standard practice.
• Students will be able to use standard software tools to create part assemblies and check for clearances.
• Students will be able to use, identify and explain standard features in solid modeling including protrusions, revolutions, cutouts, and patterns.

ME 3700 - Machine Design

• Students will be able to design machine components and assemblies including the use of common elements such as fasteners, bearings, keys, shafts and gears.
• Students will be able to analyze designs for failure in yielding under static and dynamic loads using textbook/analytical methods including the effects of combined stresses and geometric stress concentrations.
• Students will be able to select materials for designs from commonly used engineering metals based on constraints and criteria for use in mechanical part design and discuss tradeoffs in decision making in this regard.
• Students will be able to design parts based on various considerations relating to overall factor of safety and discuss the reasoning for said factors.
• Students will be able to interpret calculated results, discussing sources and effects of uncertainty, and ways to improve the subsequent risk in a design.
• Students will be able to design mechanical parts using stress-life approaches of fatigue analysis to project part life and strength based on loading scenarios, including the effects of combined and mean stresses.
• Students will be able to analyze machines and machine parts for location of critical loads and stresses and propose design changes to mitigate risk of failure or improve existing designs.
• Students will be able to estimate static and dynamic loads on parts in real-world scenarios to develop subsequent design specifications.
• Students will be able to approximate complicated scenarios with simple models, discerning the applicability and accuracy of the model.
• Students will be able to read and summarize a formal engineering specification.

ME 3800 - Mechanical Engineering Colloquium III

• Students will be able to integrate professional engineering with business, including most of the following: market awareness, customer satisfaction, quality, continuous improvement, profit, and the concepts of mission, vision and core values for a company
• Students will be able to demonstrate awareness of standards including safety, design, manufacturing, testing and quality.
• Students will be able to recognize the key elements of the entrepreneurial cycle and methods that it can be employed in entrepreneurial and intraprenuerial professional opportunities.

ME 4060 - Analysis and Design of Mechanisms

• Students will be able to analyze advanced kinematics of mechanisms including use of matrix methods.
• Students will be able to use computer software tools for mechanism design and analysis.
• Students will be able to use mechanism synthesis to design from motion requirements.
• Students will be able to explain balancing techniques.