# Course Learning Outcomes

## Department of Mathematics

Math 101 - Upon successful completion of Math 101 - Welcome Mathematics Majors, students will be able to:

- Describe several areas of mathematics beyond calculus,
- Recognize several members of the mathematics department at SUNY Geneseo
- Express their interest in mathematics, and
- Write precisely about mathematics.

Math 104 - Upon successful completion of Math 104 - Mathematical Ideas, students will be able to:

- Describe several diverse examples of mathematics not in secondary school mathematics,
- Solve problems using mathematics in unfamiliar settings, and
- Explain why mathematical thinking is valuable in daily life.

Math 112 - Upon successful completion of Math 112 - Pre-Calculus, students will be able to:

- Demonstrate algebraic facility with algebraic topics including linear, quadratic, exponential, logarithmic, and trigonometric functions,
- Produce and interpret graphs of basic functions of these types,
- Solve equations and inequalities, both algebraically and graphically, and
- Solving and model applied problems.

Math 113 - Upon successful completion of Math 113 - Finite Mathematics for Social Sciences, students will be able to

- engage in analyzing, solving, and computing real-world applications of finite and discrete mathematics,
- set up and solve linear systems/linear inequalities graphically/geometrically and algebraically (using matrices),
- formulate problems in the language of sets and perform set operations, and will be able apply the Fundamental Principle of Counting, Multiplication Principle,
- compute probabilities and conditional probabilities in appropriate ways, and
- solve word problems using combinatorial analysis.

Math 140 - Upon successful completion of Math 140 - Mathematical Concepts for Elementary Education I, a student will be able to:

- Solve open-ended elementary school problems in areas such as patterns, algebra, ratios, and percents,
- Justify the use of our numeration system by comparing it to historical alternatives and other bases, and describe the development of the system and its properties as it expands from the set of natural numbers to the set of real numbers,
- Demonstrate the use of mathematical reasoning by justifying and generalizing patterns and relationships,
- Display mastery of basic computational skills and recognize the appropriate use of technology to enhance those skills,
- Demonstrate and justify standard and alternative algorithms for addition, subtraction, multiplication and division of whole numbers, integers, fractions, and decimals,
- Identify, explain, and evaluate the use of elementary classroom manipulatives to model sets, operations, and algorithms, and
- Use number-theory arguments to justify relationships involving divisors, multiples and factoring.

Math 141 - Upon successful completion of Math 141 - Mathematical Concepts for Elementary Education II , a student will be able to:

- Solve open-ended elementary school problems in using visualization and statistical reasoning,
- Demonstrate the use of mathematical reasoning by justifying and generalizing patterns and relationships,
- Identify, explain, and evaluate the use of elementary classroom manipulatives to model geometry, probability and statistics,
- Explain relationships among measurable attributes of objects and determine measurements,
- Analyze characteristic and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships,
- Apply transformations and use symmetry to analyze mathematical situations,
- Explain and apply basic concepts of probability, and
- Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.

Math 160 - Upon successful completion of Math 160 - Media Statistics, a student will be able to:

- Critically evaluate the design, including sampling techniques, of a statistical study,
- Effectively use statistical software (e.g. MiniTab, Excel) to perform statistical computations and display numerical and graphical summaries of data sets,
- Model and analyze measurement data using the appropriate distribution, e.g. normal, binomial, chi-square,
- Compute and interpret the coefficient of correlation and the "line of best fit" for bivariate data,
- Explore relationships between categorical variables using contingency tables,
- Construct and interpret confidence intervals to estimate means and proportions for populations, and
- Apply the abilities described above to critically review articles from current newspapers , journals, and other published material.

Math 213 - Upon completion of Math 213 - Applied Calculus, a student will be able to:

- Solve systems of linear equations by use of the matrix,
- Compute limits, derivatives, and definite & indefinite integrals of algebraic, logarithmic and exponential functions,
- Analyze functions and their graphs as informed by limits and derivatives, and
- Solve applied problems using matrices, differentiation and integration.

Math 221 - Upon successful completion of MATH 221 - Calculus I, a student will be able to:

- Compute limits and derivatives of algebraic, trigonometric, inverse trigonometric, exponential, logarithmic, and piece-wise defined functions;
- Compute definite and indefinite integrals of algebraic, trigonometric, inverse trigonometric, exponential, logarithmic, and piece-wise defined functions;
- Determine the continuity and differentiability of a function at a point and on a set;
- Use the derivative of a function to determine the properties of the graph of the function and use the graph of a function to estimate its derivative;
- Solve problems in a range of mathematical applications using the derivative or the integral;
- Apply the Fundamental Theorem of Calculus; and
- Use appropriate modern technology to explore calculus concepts.

Math 222 - Upon successful completion of Math 222 - Calculus II, a student will be able to:

- Examine various techniques of integration and apply them to definite and improper integrals.
- Solve problems in a range of mathematical applications using the integral.
- Model and solve physical phenomena using integration/differential equations.
- Define, graph, compute limits of, differentiate, integrate, and solve related problems involving functions represented parametrically and in polar coordinates.
- Distinguish between the concepts of sequence and series, and determine limits of sequences and convergence and approximate sums of series.
- Define, differentiate, and integrate functions represented as power series expansions, including Taylor series, and solve related problems.

Math 223 - Upon successful completion of Math 223 - Calculus III, a student will be able to:

- Represent vectors analytically and geometrically, and compute dot and cross products for presentations of lines and planes,
- Analyze vector functions to find derivatives, tangent lines, integrals, arc length, and curvature,
- Compute limits and derivatives of functions of 2 and 3 variables,
- Apply derivative concepts to find tangent lines to level curves and to solve optimization problems,
- Evaluate double and triple integrals for area and volume,
- Differentiate vector fields,
- Determine gradient vector fields and find potential functions,
- Evaluate line integrals directly and by the fundamental theorem, and
- Use technological tools such as computer algebra systems or graphing calculators for visualization and calculation of multivariable calculus concepts.

Math 228 - Upon successful completion of Mathematics 228 - Calculus II for Biologists, within the context of biological questions a student will be able, using hand computation and/or technology as appropriate, to:

- Analyze first-order difference equations and first-order differential equations and small systems of such equations using analytic, graphical, and numeric techniques, as appropriate,
- Analyze basic population models, including both exponential and logistic growth models,
- Solve integration problems using basic techniques of integration, including integration by parts and partial fractions,
- Solve basic problems in probability theory, including problems involving the binomial, geometric, exponential, Poisson, and normal distributions,
- Estimate basic population parameters, and
- Perform a basic hypothesis test.

Math 230 - Upon successful completion of Mathematics 230 - Programming and Mathematical Problem Solving, a student will be able to:

- Write code using for/do loops, while constructions, conditional statements (if, then, else), and make use of logical constructs in the context of mathematics,
- Do basic 2- and 3-D plotting,
- Write code in the prescribed language for a number of algorithms for the topics covered given pseudo-code, or modify a given code to perform an indicated task,
- Create functions or subroutines,
- Debug code in the prescribed language at an appropriate level, and decide if they can make their code more efficient,
- Verify the correctness of a solution or decide whether the result is an acceptable approximation to the solution,
- Identify algorithms with which to solve mathematical problems, and
- Write programs from the underlying algorithms, and demonstrate the ability to employ good commenting and coding techniques.

Math 233 - Upon successful completion of Math 233 - Linear Algebra I, students will be able to:

- Solve systems of linear equations,
- Analyze vectors in R^n geometrically and algebraically,
- Recognize the concepts of the terms span, linear independence, basis, and dimension, and apply these concepts to various vector spaces and subspaces,
- Use matrix algebra and the related matrices to linear transformations,
- Compute and use determinants,
- Compute and use eigenvectors and eigenvalues,
- Determine and use orthogonality, and
- Use technological tools such as computer algebra systems or graphing calculators for visualization and calculation of linear algebra concepts.

Math 237 - Upon successful completion of Math 237 - Discrete Mathematics, a student will be able to:

- Write and interpret mathematical notation and mathematical definitions,
- Formulate and interpret statements presented in Boolean logic. Reformulate statements from common language to formal logic. Apply truth tables and the rules of propositional and predicate calculus,
- Formulate short proofs using the following methods: direct proof, indirect proof, proof by contradiction, and case analysis,
- Demonstrate a working knowledge of set notation and elementary set theory, recognize the connection between set operations and logic, prove elementary results involving sets, and explain Russell's paradox,
- Apply the different properties of injections, surjections, bijections, compositions, and inverse functions,
- Solve discrete mathematics problems that involve: computing permutations and combinations of a set, fundamental enumeration principles, and graph theory, and
- Gain an historical perspective of the development of modern discrete mathematics.

Math 239 - Upon successful completion of Math 239 - Introduction to Mathematical Proof, a student will be able to:

- Apply the logical structure of proofs and work symbolically with connectives and quantifiers to produce logically valid, correct and clear arguments,
- Perform set operations on finite and infinite collections of sets and be familiar with properties of set operations,
- Determine equivalence relations on sets and equivalence classes,
- Work with functions and in particular bijections, direct and inverse images and inverse functions,
- Construct direct and indirect proofs and proofs by induction and determine the appropriateness of each type in a particular setting. Analyze and critique proofs with respect to logic and correctness, and
- Unravel abstract definitions, create intuition-forming examples or counterexamples, and prove conjectures.
- Write solutions to problems and proofs of theorems that meet rigorous standards based on content, organization and coherence, argument and support, and style and mechanics.

Math 242 - Upon successful completion of Math 242 - Elements of Probability and Statistics, a student will be able to:

- Organize, present and interpret statistical data, both numerically and graphically,
- Use various methods to compute the probabilities of events,
- Analyze and interpret statistical data using appropriate probability distributions, e.g. binomial and normal,
- Apply central limit theorem to describe inferences,
- Construct and interpret confidence intervals to estimate means, standard deviations and proportions for populations,
- Perform parameter testing techniques, including single and multi-sample tests for means, standard deviations and proportions, and
- Perform a regression analysis, and compute and interpret the coefficient of correlation.

Math 262 - Upon successful completion of Math 262, Applied Statistics, a student will be able to:

- Identify and demonstrate appropriate sampling and data collection processes,
- Classify variables as quantitative or categorical, create appropriate numerical and graphical summaries for each type, and use these to explain/identify relationships between variables,
- Explain and successfully apply the Central Limit Theorem appropriately to describe inferences using normal distributions,
- Explain and successfully apply all aspects of parametric testing techniques including single and multi-sample tests for mean and proportion, and
- Explain and successfully apply all aspects of appropriate non-parametric tests.

Math 301 - Upon successful completion of Math 301 - Mathematical Logic, a student will be able to:

- State the following theorems and outline their proofs: The Soundness Theorem, The Completeness Theorem, The Compactness Theorem, Gödel's First Incompleteness Theorem, and Gödel's Second Incompleteness Theorem,
- Evaluate the development of 20th century Mathematical Logic in terms of its relation to the foundations of mathematics,
- Explain basic concepts from Recursion Theory, including recursive and recursively enumerable sets of natural numbers, and apply them to theoretical and appropriate applied problems in logic,
- Explain basic concepts from Proof Theory, including languages, formulas, and deductions, and use them appropriately, and
- Define and give examples of basic concepts from Model Theory, including models and nonstandard models of arithmetic, and use them in appropriate settings in logic.

Math 302 - Upon successful completion of Math 302 - Set Theory, a student will be able to:

- Discuss the development of the axiomatic view of set theory in the early 20th century,
- Identify the axioms of a system of set theory, for example the Zermelo-Fraenkel axioms, including the Axiom of Choice,
- Define cardinality, discuss and prove Cantor's Theorem and discuss the status of the Continuum Hypothesis,
- Explain basic concepts and prove basic facts about ordinals and well-ordered sets,
- Use transfinite induction to prove a selection of theorems relating to ordinals and cardinals, and
- Define the set theoretic universe V and discuss its structure.

Math 310 - Upon successful completion of Math 310 - Graph Theory, a student will be able to:

- Describe and demonstrate basic properties of graphs
- Describe the concept of isomorphic graphs and isomorphism invariant properties of graphs
- Describe knowledgeably special classes of graphs that arise frequently in graph theory
- Describe and apply the relationship between the properties of a matrix representation of a graph and the structure of the underlying graph
- Describe one real-world application of graph theory
- Apply programming skills and use mathematical software to manipulate graph models, determine basic properties of graphs, and perform basic graph algorithms
- Produce rigorous proofs of results that arise within the context of graph theory

Math 315 - Upon successful completion of Math 315 - Combinatorics, a student will be able to:

- Apply diverse counting strategies to solve varied problems involving strings, combinations, distributions, and partitions,
- Write and analyze combinatorial, algebraic, inductive, and formal proofs of combinatoric identities, and
- Recognize properties of graphs such as distinctive circuits or trees.

Math 319 - Upon successful completion of Math 319 - Number Theory, a student will be able to:

- Define and interpret the concepts of divisibility, congruence, greatest common divisor, prime, and prime-factorization,
- Apply the Law of Quadratic Reciprocity and other methods to classify numbers as primitive roots, quadratic residues, and quadratic non-residues,
- Formulate and prove conjectures about numeric patterns, and
- Produce rigorous arguments (proofs) centered on the material of number theory, most notably in the use of Mathematical Induction and/or the Well Ordering Principal in the proof of theorems.

Math 324 - Upon successful completion of Math 324 - Real Analysis I, students will be able to:

- Describe the real line as a complete, ordered field,
- Determine the basic topological properties of subsets of the real numbers,
- Use the definitions of convergence as they apply to sequences, series, and functions,
- Determine the continuity, differentiability, and integrability of functions defined on subsets of the real line,
- Apply the Mean Value Theorem and the Fundamental Theorem of Calculus to problems in the context of real analysis, and
- Produce rigorous proofs of results that arise in the context of real analysis.
- Write solutions to problems and proofs of theorems that meet rigorous standards based on content, organization and coherence, argument and support, and style and mechanics.

Math 325 - Upon successful completion of MATH 325 - Real Analysis II, a student will be able to:

- Determine the Riemann integrability and the Riemann-Stieltjes integrability of a bounded function and prove a selection of theorems concerning integration,
- Recognize the difference between pointwise and uniform convergence of a sequence of functions,
- Illustrate the effect of uniform convergence on the limit function with respect to continuity, differentiability, and integrability, and
- Illustrate the convergence properties of power series.

Math 326 - Upon successful completion of MATH 326 - Differential Equations, a student will be able to:

- Solve differential equations of first order using graphical, numerical, and analytical methods,
- Solve and apply linear differential equations of second order (and higher),
- Solve linear differential equations using the Laplace transform technique,
- Find power series solutions of differential equations, and
- Develop the ability to apply differential equations to significant applied and/or theoretical problems.

Math 328 - Upon successful completion of Math 328 - Theory of Ordinary Differential Equations, a student will be able to:

- Solve problems in ordinary differential equations, dynamical systems, stability theory, and a number of applications to scientific and engineering problems,
- Demonstrate their ability to write coherent mathematical proofs and scientific arguments needed to communicate the results obtained from differential equation models,
- Demonstrate their understanding of how physical phenomena are modeled by differential equations and dynamical systems,
- Implement solution methods using appropriate technology, and
- Investigate the qualitative behavior of solutions of systems of differential equations and interpret in the context of an underlying model.

Math 330 - Upon successful completion of Math 330 - Abstract Algebra, students will be able to:

- Assess properties implied by the definitions of groups and rings,
- Use various canonical types of groups (including cyclic groups and groups of permutations) and canonical types of rings (including polynomial rings and modular rings),
- Analyze and demonstrate examples of subgroups, normal subgroups and quotient groups,
- Analyze and demonstrate examples of ideals and quotient rings,
- Use the concepts of isomorphism and homomorphism for groups and rings, and
- Produce rigorous proofs of propositions arising in the context of abstract algebra.

Math 332 - Upon successful completion of Math 332 - Linear Programming and Operations Research, a student will be able to:

- Formulate and model a linear programming problem from a word problem and solve them graphically in 2 and 3 dimensions, while employing some convex analysis,
- Place a Primal linear programming problem into standard form and use the Simplex Method or Revised Simplex Method to solve it,
- Find the dual, and identify and interpret the solution of the Dual Problem from the final tableau of the Primal problem,
- Be able to modify a Primal Problem, and use the Fundamental Insight of Linear Programming to identify the new solution, or use the Dual Simplex Method to restore feasibility,
- Interpret the dual variables and perform sensitivity analysis in the context of economics problems as shadow prices, imputed values, marginal values, or replacement values,
- Explain the concept of complementary slackness and its role in solving primal/dual problem pairs,
- Classify and formulate integer programming problems and solve them with cutting plane methods, or branch and bound methods, and
- Formulate and solve a number of classical linear programming problems and such as the minimum spanning tree problem, the assignment problem, (deterministic) dynamic programming problem, the knapsack problem, the XOR problem, the transportation problem, the maximal flow problem, or the shortest-path problem, while taking advantage of the special structures of certain problems.

Math 333 - Upon successful completion of Math 333 - Linear Algebra II, a student will be able to:

- Analyze finite and infinite dimensional vector spaces and subspaces over a field and their properties, including the basis structure of vector spaces,
- Use the definition and properties of linear transformations and matrices of linear transformations and change of basis, including kernel, range and isomorphism,
- Compute with the characteristic polynomial, eigenvectors, eigenvalues and eigenspaces, as well as the geometric and the algebraic multiplicities of an eigenvalue and apply the basic diagonalization result,
- Compute inner products and determine orthogonality on vector spaces, including Gram-Schmidt orthogonalization, and
- Identify self-adjoint transformations and apply the spectral theorem and orthogonal decomposition of inner product spaces, the Jordan canonical form to solving systems of ordinary differential equations.

Math 335 - Upon successful completion of Math 335 - Geometry, a student will be able to:

- Compare and contrast the geometries of the Euclidean and hyperbolic planes,
- Analyze axioms for the Euclidean and hyperbolic planes and their consequences,
- Use transformational and axiomatic techniques to prove theorems,
- Analyze the different consequences and meanings of parallelism on the Euclidean and hyperbolic planes,
- Demonstrate knowledge of the historical development of Euclidean and non-Euclidean geometries,
- Use dynamical geometry software for constructions and testing conjectures, and
- Use concrete models to demonstrate geometric concepts.

Math 338 - Upon successful completion of Math 338 - Topology, a student will be able to:

- Define and illustrate the concept of topological spaces and continuous functions,
- Define and illustrate the concept of product topology and quotient topology,
- Prove a selection of theorems concerning topological spaces, continuous functions, product topologies, and quotient topologies,
- Define and illustrate the concepts of the separation axioms,
- Define connectedness and compactness, and prove a selection of related theorems, and
- Describe different examples distinguishing general, geometric, and algebraic topology.

Math 340 - Upon successful completion of Mathematics 340/Biology 340 - Modeling Biological Systems, a student will be able to:

- Describe standard modeling procedures, which involve observations of a natural system, the development of a numeric and or/analytical model, and the analysis of the model through analytical and graphical solutions and/or statistical analysis,
- Distinguish between analytic and numerical models,
- Distinguish between stochastic and deterministic models,
- Use software to quantitatively test hypotheses with data and build and evaluate mathematical and simulation models of biological systems,
- Present an oral report of a semester-long group project involving the development and the analysis of a model of a biological system, and
- Assess the value of model results discussed in the news and in scientific and mathematical literature.

Math 341 - Upon successful completion of Math 341 - Probability and Applied Statistics, a student will be able to:

- Recognize the role of and application of probability theory, descriptive and inferential statistics in many different fields,
- Define, illustrate, and apply the concepts of probability and conditional probability,
- Define, illustrate, and apply the concepts of discrete and continuous random variables,
- Define, illustrate, and apply the concept of expectation to the mean, variance, and covariance of random variables,
- Identify and demonstrate appropriate sampling and data collection processes, classification of variables, and graphical summaries,
- Apply parametric testing techniques including single and multi-sample tests for mean and proportion and regression, and
- Use statistical software for probability simulations and data analysis.

Math 342 - Upon successful completion of Math 342: Statistical and Machine Learning, a student will be able to:

- Understand the mathematical foundations behind statistical and algorithmic modeling;
- Understand the practices of statistical and algorithmic modeling;
- Understand and apply statistical and machine learning methods including:
- regression (linear, nonlinear, parametric, nonparametric, generalized additive models),
- supervised and unsupervised learning (classification, tree-based methods, Support Vector Machine, neural and multi-layer networks), and
- some industry-standard algorithms;

- build high performance predictive models and improve using bagging, boosting, and regularization;
- apply data science and computational skills in data management with state-of-the-art programming languages such as R and Python; and
- research a topic of interest with real-world data, implement statistical and machine learning models, write up a report, and present the results.

Math 343 - Upon successful completion of Math 343: Advanced Applied Statistics, a student will be able to:

- review random variables and vectors;
- recognize the theory of multivariate statistics;
- know, apply and critique factor analysis, classification and clustering methods;
- build multivariate statistical models, evaluate the performances, and interpret the results;
- apply cutting-edge statistical models to an individually chosen project with real-world data;
- implement modeling data techniques using statistical packages, R and SAS/SPSS; and
- write up a statistical data analysis report, and present the results.

Math 345 - Upon successful completion of Math 345 - Numerical Analysis I, a student will be able to:

- Derive numerical methods for approximating the solution of problems of continuous mathematics,
- Analyze the error incumbent in any such numerical approximation,
- Implement a variety of numerical algorithms using appropriate technology, and
- Compare the viability of different approaches to the numerical solution of problems arising in roots of solution of non-linear equations, interpolation and approximation, numerical differentiation and integration, solution of linear systems.

Math 346 - Upon successful completion of Math 346 - Numerical Analysis II, a student will be able to:

- Derive numerical methods for approximating the solution of problems of continuous mathematics,
- Analyze the error incumbent in any such numerical approximation,
- Implement a variety of numerical algorithms using appropriate technology, and
- Compare the viability of different approaches to the numerical solution of problems arising in roots of solution of non-linear equations, interpolation and approximation, numerical differentiation and integration, solution of linear systems.

Math 348 - Students in Math 348 - Oral Presentation and Research Seminar will:

- Demonstrate library research skills in the area of mathematics,
- Critique mathematical presentations, and
- Produce a mature oral presentation of a non-trivial mathematical topic.

Math 350 - Upon successful completion of Math 350 - Vector Analysis, a student will be compute and analyze:

- Scalar and cross product of vectors in 2 and 3 dimensions represented as differential forms or tensors,
- The vector-valued functions of a real variable and their curves and in turn the geometry of such curves including curvature, torsion and the Frenet-Serre frame and intrinsic geometry,
- Scalar and vector valued functions of 2 and 3 variables and surfaces, and in turn the geometry of surfaces,
- Gradient vector fields and constructing potentials,
- Integral curves of vector fields and solving differential equations to find such curves,
- The differential ideas of divergence, curl, and the Laplacian along with their physical interpretations, using differential forms or tensors to represent derivative operations,
- The integral ideas of the functions defined including line, surface and volume integrals - both derivation and calculation in rectangular, cylindrical and spherical coordinate systems and understand the proofs of each instance of the fundamental theorem of calculus, and
- Examples of the fundamental theorem of calculus and see their relation to the fundamental theorems of calculus in calculus 1, leading to the more generalised version of Stokes' theorem in the setting of differential forms.

Math 360 - Upon successful completion of Math 360 - Probability, a student will be able to:

- Recognize the role of probability theory, descriptive statistics and inferential statistics in the applications of many different fields,
- Define and illustrate the concepts of sample space, events and compute the probability and conditional probability of events, and use Bayes' Rule,
- Define, illustrate and apply the concepts of discrete and continuous random variables, the discrete and continuous probability distributions and the joint probability distributions,
- Apply Chebyshev's theorem,
- Define, illustrate and apply the concept of the expectation to the mean, variance and covariance of random variables,
- Define, illustrate and apply certain frequently used discrete and continuous probability distributions, and
- Illustrate and apply theorems concerning the distributions of functions of random variables and the moment-generating functions.

Math 361 - Upon successful completion of Math 361 - Statistics, a student will be able to:

- Recall the basic concepts in probability and statistics and understand the concept of the transformation of variables and moment-generating functions,
- Define and examine the random sampling (population and sample, parameters and statistic) data displays and graphical methods with technology,
- Recognize and compute the sampling distributions, sampling distributions of means and variances (S2) and the t- and F-distributions,
- Understand, apply and compute in one- and two- sample estimation problems,
- Understand, apply and compute maximum likelihood estimation,
- Understand, apply and compute in one- and two- sample tests of hypotheses problems,
- Recognize the relationship between the confidence interval estimation and tests of hypothesis,
- Understand, apply and examine the goodness-of-fit test, test for independence, and homogeneity,
- Recognize the basic concepts of simple linear regression and correlation, and
- Recognize the concept of the analysis-of-variance technique and the strategy of experimental design.

Math 366 - Upon successful completion of Math 366 - Mathematical Foundations of Actuarial Science, a student will be able to use and apply the following concepts in a risk management context:

- General probability, Bayes Theorem/Bayes Theorem / Law of total probability,
- Univariate probability distributions,
- Multivariate probability distributions,
- Moment generating functions,
- Transformations,
- Order Statistics, and
- Risk management concept.

Math 371 - Upon successful completion of Math 371 - Complex Analysis, a student will be able to:

- Represent complex numbers algebraically and geometrically,
- Define and analyze limits and continuity for complex functions as well as consequences of continuity,
- Apply the concept and consequences of analyticity and the Cauchy-Riemann equations and of results on harmonic and entire functions including the fundamental theorem of algebra,
- Analyze sequences and series of analytic functions and types of convergence,
- Evaluate complex contour integrals directly and by the fundamental theorem, apply the Cauchy integral theorem in its various versions, and the Cauchy integral formula, and
- Represent functions as Taylor, power and Laurent series, classify singularities and poles, find residues and evaluate complex integrals using the residue theorem.

Math 372 - Upon successful completion of Math 372 - Partial Differential Equations, a student will:

- Be familiar with the modeling assumptions and derivations that lead to PDEs,
- Recognize the major classification of PDEs and the qualitative differences between the classes of equations, and
- Be competent in solving linear PDEs using classical solution methods.

Math 380 - Upon successful completion of this special topics course, a student will:

- Be conversant with the specialized vocabulary of the topic,
- Be adept with manipulation of the standard notation of the topic,
- Be able to solve routine problems specific to the topic,
- Be able to quote the important assumptions and results (main theorems) of the topic,
- Be able to rigorously prove results specific to the topic, and
- Appreciate the relationship of this topic to the undergraduate mathematics program

Math 382 - Upon successful completion of MATH 382 - Discrete Wavelets and Applications, a student will be able to:

- Apply calculus, linear algebra, and mathematical transforms to real-world problems,
- Upload and manipulate digital images and audio files,
- Explain the connection between complex numbers and Fourier transforms to convolutions, filters, and their properties,
- Derive properties of orthogonal and bi-orthogonal wavelet transforms, and apply them to real-world problems,
- Apply programming skills and use mathematical software as a discovery tool and to solve a real-world problem, and
- Research a topic in the application of wavelets, code the solution, write up the results, and present the results.

Math 383 - Upon successful completion of Mathematics 383 - Biomathematics Seminar, a student will be able to:

- Discuss applications of mathematics and computational approaches to questions involving biological phenomena,
- Explain the contribution of a scientific paper to the field of biomathematics,
- Develop and lay the foundation to the solution of a problem in biomathematics, and
- In addition, seniors taking this course to fulfill the seminar requirement in the biology degree program should expect to develop and write a grant proposal to do research in the area of biomathematics.

Math 390 - Upon successful completion of MATH 390 - History of Mathematics, a student will be able to:

- Trace the development and interrelation of topics in mathematics up to the undergraduate level,
- Discuss mathematics in historical context with contemporary non-mathematical events,
- Analyze historical mathematical documents - interpret both the concepts of the text and the methods of mathematics, and
- Identify significant contributions in mathematics from women and from outside of Europe.

Math 393 - Students in Math 393 - Honors Thesis Independent Study will:

- Engage in the study or research of a topic that is beyond the regular math department offerings in both rigor and content, and
- Produce a document (paper or honors thesis) that exhibits both the background and the conclusions reached as a result such study or research.

INTD 301 - Upon successful completion of INTD 301 - Topics in Secondary Education: Mathematics, students will be able to:

- Create and solve sophisticated multi-step problems in various topics from the secondary curriculum,
- Construct multiple representations for selected topics from arithmetic, algebra, geometry, trigonometry, probability, and statistics,
- Make connections between concepts in different areas of mathematics and between the mathematics of undergraduate courses and the mathematics of the secondary curriculum, and
- Recognize current and historical types of mathematics assessment in New York state and be prepared to implement curricular programs that address these needs and those of their students.

INTD 302 - Upon successful completion of INTD 302 - Methods and Materials: Mathematics, students will:

- Be familiar with current standards (state, national, and NCTM), both content and process, for the secondary mathematics curriculum,
- Be able to do both short and long term planning of lessons and units that meet current standards for the secondary mathematics curriculum,
- Have taught mathematics lessons which they have planned to small groups of fellow students and/or area 7-12 students,
- Be able to assess student learning in mathematics,
- Be able to find research on the teaching and learning of content in the secondary mathematics curriculum and analyze teaching ideas and textbook presentations of said content in light of the found research, and
- Be familiar with technology currently used in the mathematics classroom.