Department of
Mathematicsand Computer Science |
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Department of Mathematics and Computer Science

Course Goals and Objectives

- Mission Statement
- General Departmental Goals and Objectives of Courses
- Core Curriculum Learning Goals and Objectives for Mathematics Courses
- General Information for All Syllabi
- Specific Course Goals and Objectives

**Mission Statement:** The Department of Mathematics and Computer
Science promotes the methods and benefits of rigourous, objective mathematical
thought, theoretical computer science and algorithmic and logical understanding,
both for their intrinsic beauty and for their applications to other disciplines.
These principles are incorporated into the larger University program of educating the whole person in the Jesuit tradition. Our aims are focused not only on our students, but also on our professional communities and the community at large.

**General Departmental Goals and Objectives of Courses**

*Link to Complete List of Goals and Objectives for
the Department.*

*Link to Chart Relating Course Goals and Objectives to
Specific Courses.*

Goal 1: Connect the study of mathematics and computer science to other disciplines.

Objective:

a) Students will obtain skills and logical perspectives in our introductory (core) courses that prepare them for subsequent courses inside and outside our department. Specifically, students will develop proficiency with the techniques of mathematics and/or computer science, the ability to evaluate logical arguments, and the ability to apply mathematical methodologies to solving real world problems.Goal 2: For students who choose to pursue a degree in Mathematics: Appreciate and develop facility with mathematical structures.

Objectives:

a) Students must be able to understand and write rigorous arguments (i.e., proofs) for theorems.Goal 3: For students who choose to pursue a degree in Computer Science: Understand the foundations of Computer Science and appreciate some of its theoretical and applied uses.b) Students must show mastery in the three basic areas of mathematics: analysis, algebra, and topology /geometry on a basic level in lower division courses and at an advanced level in upper division courses.

Objectives:

a) Students will develop a strong foundation in programming, software development and data manipulation and become familiar with theoretical aspects of computer science.b) Students will acquire a strong facility for developing, analyzing, and applying algorithms.

* Pre-fall 2014*

Goals: Critical Thinking, Mathematics and Quantitative Reasoning

Objectives: Students will:

1.1 Demonstrate their problem solving skills, including their ability to interpret problem situations, choose among several potentially appropriate mathematical methods of solution, persist in the face of difficulty, and present full and cogent solutions that include appropriate justification for their reasoning.

1.2 Understand and be able to articulate the differences between inductive and deductive reasoning. In particular, students will appreciate the role of mathematical proof in formalizing deductive reasoning and as a means of conveying mathematical knowledge, and to understand the differences between proofs and other less formal arguments.

1.3 Utilize and describe mathematical ideas from multiple perspectives, including the internal connections between geometry, algebra, and numerical computation, as well as the connections between theory and applications. This flexibility should be evident in students' approach to problem solving as well as their ability to communicate their solutions and methods.

1.4 Demonstrate an understanding of mathematical content (including the limits to its application) that goes beyond mere fluency in using mathematical symbols, language and formulas.

Goals: Critical Thinking, Mathematics and Quantitative Reasoning, Communication, Complexity

Objectives: Students will:

1.1 Demonstrate problem solving skills, such as the ability to determine what a problem is asking, choose among several potentially appropriate mathematical methods of solution, and present solutions that include appropriate justification.

1.2 Demonstrate their understanding of mathematical ideas from multiple perspectives, such as by (a) using the internal connections between geometry, algebra, and numerical computation, (b) applying the connections between theory and applications, or (c) distinguishing between a formal proof and a less formal arguments and understanding the different roles these play in mathematics.

1.3 Demonstrate an understanding of mathematical content (including the limits to its application) that goes beyond mere fluency in using mathematical symbols, language and formulas.

**General Information for All Syllabi**

**Academic Integrity:** The penalty for cheating may be a failing grade for the course, and the University may take further disciplinary action. All of the work that you turn in should be your own, and not that of a classmate or copied from another source. Please see
http://www.scu.edu/studentlife/resources/academicintegrity/index.cfm
for further information.

**Disability accommodation policy:** To request academic accommodations for a disability, students must contact the Disability Resources Office located in Benson room 216, (408) 554-4111; TTY (408) 554-5445. Students must provide documentation of a disability to Disability Resources prior to receiving accommodations.

**Specific Course Goals and Objectives**

**Prenotes:**

(1) In addition to providing you with a good foundation in a fundamental area of mathematics, all mathematics courses, especially those designated as fulfilling the Santa Clara Core, will also contribute to a student's skills and logical perspective that will be applicable to many other courses requiring mathematical methods and careful reasoning.

(2) In most mathematics courses, all assignments, quizzes, and exams foster all core learning goals, the departmental goals, and the course goals.

- CS 3 -- Introduction to Computing and Applications
- Math 4 (formerly 41) -- The Nature of Mathematics
- Math 6 -- Finite Mathematics for Social Science
- Math 7 -- Calculus for Social Science
- Math 8 -- Introduction to Statistics
- Math 9 -- Precalculus
- CS 10 -- Introduction to Computer Science
- Math 11 -- Calculus and Analytic Geometry I
- Math 12 -- Calculus and Analytic Geometry II
- Math 13 -- Calculus and Analytic Geometry III
- Math 14 (formerly 21) -- Calculus and Analytic Geometry IV
- Math 21 (to be renumbered 14 in Fall 2009) -- Calculus and Analytic Geometry IV
- Math 22 -- Differential Equations
- Math 30 -- Calculus for Business I
- Math 31 -- Calculus for Business II
- Math 32 -- Mathematical Logic
- Math 41 (to be renumbered 4 in Fall 2009) -- The Nature of Mathematics
- Math 44 -- Mathematics for Elementary Teachers I
- Math 45 -- Mathematics for Elementary Teachers II
- Math 51/COEN 19 -- Discrete Mathematics
- Math 52 -- Introduction to Abstract Algebra
- Math 53 -- Linear Algebra
- CS 60 -- Object-oriented Programming
- CS 61 -- Data Structures
- Math/CS 90 -- Lower-Division Seminars
- Math 100 -- Writing in the Mathematical Sciences
- Math 101 -- A Survey of Geometry
- Math 102 -- Advanced Calculus
- Math 103 -- Linear Algebra II
- Math 105 -- Theory of Functions of a Complex Variable
- Math 111 -- Abstract Algebra I
- Math 112 -- Abstract Algebra II
- Math 113 -- Topology
- Math 122 -- Probability and Statistics I
- Math 123 -- Probability and Statistics II
- Math 125 -- Mathematical Finance
- Math 133 -- Logic and Foundations
- Math 134 -- Set Theory
- Math 144 -- Partial Differential Equatiions
- Math 153 -- Intermediate Analysis I
- Math 154 -- Intermediate Analysis II
- Math 155 -- Ordinary Differential Equations
- CS 161 -- Theory of Automata and Languages I
- CS 162 -- Theory of Automata and Languages II
- CS 163/COEN 179 -- Theory of Algorithms
- CS 164 -- Computer Simulation
- Math/CS 165 -- Linear Programming
- Math/CS 166 -- Numerical Analysis
- CS 167 -- Switching Theory and Boolean Algebra
- CS 168 -- Computer Graphics
- CS 169 -- Programming Languages
- Math 170 -- Development of Mathematics
- Math 172 -- Problem Solving
- Math 174 -- Differential Geometry
- Math 175 -- Theory of Numbers
- Math 176 -- Combinatorics
- Math 177 -- Graph Theory
- Math 178 -- Cryptography
- CS 181 -- Applied Cryptography
- CS 182 -- Digital Steganography
- Math/CS 190 -- Upper-Division Seminars
- Math/CS 196 -- Advanced Topics
- Math/CS 198 -- Internship/Practicum
- Math/CS 199 -- Independent Study

Specific Goals and Objectives: This course will contribute to students' skills in mathematical thinking and careful, logical reasoning that are applicable to many other courses. The students will be asked to explore elementary mathematical ideas, in much the same way that mathematicians do mathematical research, so that they may see for themselves the excitement of making a mathematical discovery, and understand the beauty, and power, of mathematics as it is used to describe objects and situations in the real world. This course will help students to "think about mathematics in a new way" (quoting a satisfied former Math 41 student).

**Math 6 -- Finite Mathematics for Social Science**

*Fulfills Mathematics Core Requirement*

**General Departmental Goals and Objectives:** 1a; 2b

Specific Goals and Objectives:
In this course students

- will practice effective communication and interaction skills.
- as part of classroom learning, will interpret problem situations, choose among several appropriate mathematical methods of solution, persist to a solution and present solutions verbally and in written form that include appropriate justification for your reasoning.
- on assignments and tests, will need to be able to formalize deductive reasoning, make connections between theory and applications, and demonstrate an understanding of mathematical content beyond symbols and formulas.

**Math 7 -- Calculus for Social Science**

*No longer offered as of Fall 2013*

**General Departmental Goals and Objectives:** 1a; 2b

Specific Goals and Objectives: In this course, students will apply
the methods of differential and integral calculus to solve a variety of
problems particularly applicable to the social sciences and
to explain their reasoning.

- Students will use the derivative as an important problem-solving tool for real-world situations. Students will also briefly look at indefinite and definite integrals.
- Students will predict properties of curves from their derivative.
- Students will be able to explain how differential calculus combines geometric ideas of slope, real-world concepts of rates and analytical concepts of derivatives to give a unified perspective of mathematics.
- Beyond computational proficiency, students will be led to understand the meaning of results, as well as central theorems of mathematics.

Specific Goals and Objectives: In this course, students will practice effective communication and interaction skills. As part of classroom learning students will interpret problem situations, choose among several appropriate mathematical methods of solution, persist to a solution and present solutions verbally and in written form that include appropriate justification for your reasoning. On assignments and tests students will need to be able to formalize deductive reasoning, make connections between theory and applications, and demonstrate an understanding of mathematical content beyond symbols and formulas.

In addition to providing you with a good foundation in a fundamental area of mathematics, this course will also contribute to a student's skills and logical perspective that will be applicable to many other courses requiring mathematical methods and careful reasoning.

Upon successful completion of this course, a student will be able to:

- explain the basic concepts of statistics
- summarize numeric data by computing descriptive statistics
- apply basic probability theory
- explain confidence intervals
- test hypotheses applying probability theory
- explain the differences among various statistical techniques and identify an appropriate technique for a given set of variables and research questions
- use a calculator as a tool in statistical analysis

Specific Goals and Objectives: In this course, students will obtain a good foundation in algebra, trigonometry, and analytical geometry. This course will also contribute to students' skills and logical perspective that will be applicable to many other courses requiring mathematical methods and careful reasoning.

**CS 10 -- Introduction to Computer Science**

**General Departmental Goals and Objectives:** 1a; 3a; 3b

Specific Goals and Objectives:
In this course, students will develop:

1. proficiency in basic algorithm extraction. Given a problem
statement, be able to extract the given data as input, formulate a
clear
goal or desired output, and lay out a set of instructions to go from
input to output.

2. competence with the fundamental flow control structures of
branching, looping, subroutine, and recursion as well as the data
structures of variables and arrays. Be able to demonstrate an ability
to
read and write code using these structures.

3. understanding of the moral issues involved in computing and
the role it plays in our society.

4. a capacity to work with object oriented programming at the
introductory level as demonstrated by the ability to read and write
code
involving classes and objects.

**Math 11 -- Calculus and Analytic Geometry I**

*Fulfills Mathematics Core Requirement*

**General Departmental Goals and Objectives:** 1a; 2b

Specific Goals and Objectives: In this course students will apply the methods of differential calculus to solve a variety of problems and to explain their reasoning.

- (CG/CG14 1.1) Students will use the derivative as an important problem-solving tool.
- (CG 1.2/CG14 1.2c) Students will predict properties of curves from their derivative.
- (CG 1.3/CG14 1.2a,b) Students will be able to explain how differential calculus combines geometric ideas of slope, real-world concepts of rates and analytical concepts of derivatives to give a unified perspective of mathematics.

Specific Goals and Objectives: In this course, focusing on integral calculus,

- emphasis will be placed on the use of the definite and indefinite integral as an important problem-solving tool.
- students will learn to predict properties of functions from their antiderivatives.
- integral calculus will be seen to combine geometric ideas of area and analytic concepts of the indefinite integral to give a unified perspective of mathematics.
- beyond computational proficiency, students will be led to understand the meaning of results, as well as central results such as the Fundamental Theorems of Calculus.

Specific Goals and Objectives: In this course, focusing on topics in discrete mathematics,

- emphasis will be placed on using results from previous calculus courses to solve more complex problems.
- students will learn to find infinite power series to approximate functions and also some non-elementary integrals involving them.
- students will have multiple opportunities to analyze problems from analytical, geometric, and numerical perspectives.
- beyond computational proficiency, students will strive to understand the meaning of our results, as well as encountering some central theorems of mathematics.

Specific Goals and Objectives: In this course, focusing on calculus concepts applied to surfaces in 3-dimensions on other calculus concepts,

- emphasis will be placed on the use of integrals and multivariable calculus as an important problem-solving tool.
- students will learn to analyze surfaces, using partial derivatives, and their volumes by studying properties of their antiderivatives.
- students will combine geometric visualization (of 2 dimensional curves and 3 dimensional surfaces) with careful analytical reasoning to solve problems and connect our ideas to other disciplines.
- beyond computational proficiency, students will strive to understand the meaning of our results, as well as encountering some central theorems of mathematics.

Specific Goals and Objectives: In this course, students

- will be able to categorize Ordinary Differential Equations (ODEs): order, linear vs. nonlinear, homogeneous vs. nonhomogeneous, etc.
- will, within each category, master techniques to solve ODEs;
- will connect material both to other courses within the department and to phenomena from other disciplines.

Specific Goals and Objectives: In this course, students will apply the methods of differential calculus to solve a variety of problems particularly applicable to the world of business and to explain their reasoning.

- (CG/CG14 1.1) Students will use the derivative as an important problem-solving tool for real-world situations.
- (CG 1.2/CG14 1.2c) Students will predict properties of curves, and thus of rates of change, from their derivative.
- (CG 1.3/CG14 1.2ab) Students will be able to explain how differential calculus combines geometric ideas of slope, real-world concepts of rates and analytical concepts of derivatives to give a unified perspective of mathematics.

Specific Goals and Objectives: In this course, students will connect calculus to the world of finance, economics, and other fields of business. Success will be measured by a student's ability to apply specific techniques to real-world problems. These techniques include 1) finding antiderivatives, 2) evaluating definite integrals, 3) computing partial derivatives, 4) optimizing functions of several variables, with and without constraints, and 5) computing probabilities in situations that involve continuous random variables.

Specific applications include salary accumulation, consumers. surplus, the Gini index, present value of future income, optimization of profit, minimization of costs, and risk analysis.

Students will also be asked to show mastery of various logical relationships among quantities, especially those at play in the Fundamental Theorem of Calculus.

All these areas bring together the three basic areas of mathematics: analysis, algebra, and geometry; in the text for the course, these are called numerical, algebraic, and graphical points of view.

Specific Goals and Objectives: This course will contribute to students' skills in mathematical thinking and careful, logical reasoning that are applicable to many other courses. The students will be asked to explore elementary mathematical ideas, in much the same way that mathematicians do mathematical research, so that they may see for themselves the excitement of making a mathematical discovery, and understand the beauty, and power, of mathematics as it is used to describe objects and situations in the real world. This course will help students to "think about mathematics in a new way" (quoting a satisfied former Math 41 student).

**Math 44 -- Mathematics for Elementary Teachers I**

**General Departmental Goals and Objectives:** 1a; 2b; 3b

Specific Goals and Objectives: In this course, students will:

- learn problem-solving techniques and become proficient and confident in solving problems;
- learn to communicate effectively about mathematics, both verbally and in writing;
- reaffirm and strenghten their foundation in arithmetic, learning
*why*things work the way that they do.

Specific Goals and Objectives: In this course, students will:

- learn problem-solving techniques and become proficient and confident in solving problems;
- learn to communicate effectively about mathematics, both verbally and in writing;
- reaffirm and strengthen your foundation in the various mathematics content standards for the elementary level, emphasizing the whys as well as alternatives to standard approaches.

Specific Goals and Objectives: In this course, students will gain "mathematical maturity" -- in particular the ability to create and comprehend mathematical arguments. We will focus on mathematical arguments in various areas; in each area, students will build up requisite background knowledge (often useful by itself), culminating in the students being able to:

- Prove (or disprove) that two propositions are logically equivalent.
- Prove that two sets are equal.
- Determine if a function is invertible.
- Determine the next term in a sequence, total complicated summations, and encrypt and decrypt secret messages.
- Count how many passwords are possible given certain constraints, count how many ways one can get particular poker hands, etc.

Specific Goals and Objectives: This is a transition courses from the calculus sequence, which deals with relatively concrete applications of mathematics to science and engineering, to, as the name this course implies, an introduction to abstract mathematics, with emphasis on structure and on proving theorems from given definitiions and axiioms. Students succeeding in this course will develop a new way of thinking, more representative of modern mathematics than the basic calculus courses provide.

**Math 53 -- Linear Algebra**

**General Departmental Goals and Objectives:** 1a; 2b; 3b

Specific Course Goals and Objectives: In this course, students will learn to:

- solve problems, including choosing and developing appropriate methods, as well as communicating mathematical ideas effectively. Emphasis will be placed on the use of matrix theory as an important problem-solving tool;
- use mathematical reasoning and deduction to draw valid conclusions from given information; for example, students will learn to predict the nature of solution sets of linear systems using matrix theory;
- use and understand mathematical ideas from multiple and interconnected perspectives, including algebraic, geometric, analytical and numerical points of view. Linear algebra combines geometric ideas of vectors spaces, solutions to systems of linear equations, and fundamental concepts of eigenvectors and eigenvalues ini pure and applied mathematics to give a unified perspective of mathematics;
- understand significant mathematical ideas and results in addition to mastering computational techniques. In addition to knowing how to carry out a certain procedure, students will learn when that procedure is appropriate and, most importantly, why it works. Students will strive to understand the meaning of results, as well as encounter some central theorems of mathematics.

Specific Course Goals and Objectives: In this course, students will be able to

- understand and practice the basic tenets of object-oriented programming;
- use, design, and implement abstract data types; and
- develop graphical user interfaces usiing C++ and Qt.

**CS 61 -- Data Structures**

**General Departmental Goals and Objectives:** 3a; 3b

Specific Course Goals and Objectives:
By the end of this course students will be able to

- specify, design, and implement basic data structures such as stacks, queues, binary trees, heaps, hash tables, graphs; and
- understand and implement basic searching and sorting algorithms using these data structures.

This course will fulfill the Advanced Writing requirement in the Core Curriculum. As such, it will help students to achieve some overarching goals, and some specific objectives relevant to advanced writing.

Specific Course Goals: Critical Thinking, Complexity, Communication

Specific Course Objectives: Students who have completed Advanced Writing will

- Be proficient in reading and writing with a critical point of view that demonstrates depth of thought and a thorough understanding of the rhetorical situation. (Critical Thinking, Complexity, Communication)
- Write essays that contain well-supported, arguable theses and that demonstrate personal engagement and clear purpose. (Critical Thinking, Complexity, Communication)
- Be proficient in independently and deliberately locating, selecting, and appropriately using and citing evidence that is ample, credible, and smoothly integrated into intellectually honest writing appropriate to a particular discipline. (Complexity, Communication; Meta-Goal: Information Literacy)
- Use writing processes as modes of thinking and learning that can be generalized across a range of writing and thinking tasks. (Critical Thinking, Complexity; Meta-Goals: Intentional Learning)

Specific goals and objectives: Through this course, students will

- Demonstrate general understanding of Euclidean, hyperbolic, and spherical geometry
- Show mastery in one area chosen from these
- Understand and write rigorous arguments, reasoning from axioms to theorems

Specific Goals and Objectives: This course is intended as a bridge course between the science/engineering calculus sequence and the highly intensive real analysis courses (Math 153, 154), It is both a review courses and a course with new material. Concepts from calculus such as limits are again examined here, but this time the subtle concept of epsilons and deltas are delved into. New, more advanced materials, such as elliptic integrals, Jacobians, Green's theorem, etc., are also covered. Students should become more comfortable with the details behind the applications of calculus.

Specific Goals and Objectives: In this course, students will synthesize related mathematical objects such as matrices, polynomials, and

Specific Goals and Objectives: In this course, students will learn how to

- understand the interplay between the geometry of the plane and the arithmetic of complex numbers.
- Integrate previous notions of derivatives, logarithms, vectors, line integrals, and power series from the calculus sequence with their complex counterparts, and understand how the complex versions generalize and sometimes simplify the earlier notions.

Specific Goals and Objectives: In this course, students will be expected to

- learn, understand, and communicate definitions, examples, fundamental theorems and applications relevant to the study of groups, and
- analyze, develop, and communicate rigorous mathematical proofs of statements concerning groups.

Specific Goals and Objectives: In this course, students will be expected to

- learn, understand, and communicate definitions, examples, fundamental theorems and applications relevant to the study of rings and fields, and
- analyze, develop, and communicate rigorous mathematical proofs of statements concerning rings and fields.

Specific Goals and Objectives: In this course, students will be expected to

- learn, understand, and communicate definitions, examples, fundamental theorems and applications relevant to the study of topological spaces, and
- analyze, develop, and communicate rigorous mathematical proofs of statements in topology and related fields.

Specific Goals and Objectives: In this course, students will be expected to

- learn, understand, and communicate definitions, examples, fundamental theorems and applications relevant to the study of probability, and
- analyze, solve, and communicate solutions to problems in probability.

Specific Goals and Objectives: In this course, students will be expected to

- learn, understand, and communicate definitions, examples, fundamental theorems and applications relevant to the study of mathematical statistics, and
- analyze, solve, and communicate solutions to problems in mathematical statistics.

Specific Goals and Objectives: In this course, students will be expected to

- understand the basic principles of finance and economic investments, which they can apply to their own investing or a companies.
- see how probability and differential equations combine to understand processes with white noise. This generates the noise not only in stock market prices, but also the noise in radar signals, movements of microscopic particles in physics, chemistry, and biology, etc.
- understand the principles of control theory/ dynamic optimization, which means how to continuously change a control to optimize an outcome. This is used not only in finance, but also throughout engineering and is central to the field of operations research.
- appreciate how their background prepares them for tackling new mathematics and computional methods as applied to financial applications they have likely not thought about before.

Specific Course Goals and Objectives: In this course, students will be expected to:

- see how physics and PDEs are fundamentally related. PDE are the natural result of modeling certain phenomena in physics. Solving PDEs can tell us about the behavior of physical problems. Physics can tell us which solution of a PDE is desired.
- understand the difference between the behavior of solutions to the Laplace (elliptic), Heat (parabolic), and Wave (hyperbolic) equations.
- learn to interpret, and manipulate Fourier Series.
- understand the difference between linear and nonlinear equations and begin to understand the behavior of some nonlinear equations such as some image processing PDE and first order nonlinear hyperbolic equations.

Specific Course Goals and Objectives: In this course, students will connect the study of mathematics to other disciplines and obtain skills and logical perspectives that prepare them for subsequent courses in mathematics and other sciences. Topics will include systems of linear differential equations, two-dimensional autonomous systems, and existence theory.

**CS 161 -- Theory of Automata and Languages I**

**General Departmental Goals and Objectives:** 2a; 3a; 3b

Specific Goals and Objectives: In this course, students will learn how
to

- understand formal machine models for recognizing strings;
- formulate finite descriptions for many (infinite) sets of strings using these machine models;
- convert among equivalent descriptions;
- prove that no formal descriptions exist for certain sets of strings.

Specific Goals and Objectives: In this course, students will learn how to

1. Develop proficiency in the formulation of algorithm operation count. Given an iterative code be able to express the operation count as a summation. Given a recursive code be able to formulate the operation count as the solution to a recurrence relation.

2. Be able to solve common summation equations and recurrence equations.

3. Understand the definitions of complexity class. Be able to prove basic properties of complexity classes, such as containment or determining membership, using their definition.

4. Develop an understanding of the basic algorithm formulation methodologies, such as decrease and conquer, transform and conquer, and dynamic programming, as evidenced by the capacity to formulate creative algorithms employing these ideas.

5. Develop familiarity with the most common algorithms to all computer scientists, including algorithms for searching, sorting, graph processing, and for solving geometric and numerical problems, as evidenced by the ability to utilize and modify these algorithms to solve complex problems.

6. Develop a basic understanding of deterministic versus non-deterministic polynomial time algorithms, as evidenced by the capacity to recognize problems which are unlikely to have polynomial time solutions.

Specific Goals and Objectives: By the end of this course, students will be able to:

- generate random variates for various standard probability distributions;
- evaluate randomness of observed data using the chi-square and Kolmogorov-Smirnov tests;
- implement discrete-event simulations of queueing systems and integral evaluations;
- estimate distribution properties of simulation outcomes; and
- speed up simulations using variance-reduction techniques.

Specific Goals and Objectives: Since the optimal allocation of money, manpower, energy, or a host of other scares factors, is of importance to decisions made in many disciplines, this course will attempt to derive computation methods for solving models of real world problems.

Specific Goals and Objectives: In this course, students will study algorithms and methods to obtain numerical results to common mathematical problems both accurately and efficiently. Where appropriate, students will see how various numerical problems can be understood analytically and geometrically to aid in obtaining a solution method. In particular, students will

- learn about the power of various numerical methods, the pros and cons of different numerical algorithms, and the sources of numerical errors.
- find numerical roots of non-linear equations and solutions of systems of linear equations, both directly and iteratively, and learn about convergence rates and conditioning problems.
- perform numerical integration and find solutions to differential equations numerically.
- approximate data by various functions and fit functions to data points via cubic splines and other functions.
- study other numerical problems (e.g., finding eigenvalues, orthogonal polynomials) as time permits.

Specific Goals and Objectives: By the end of this course students will be able to

i) use the OpenGL API to develop simple 2-D and 3-D graphics applications;

ii) implement features supported by such an API such as rasterization, clipping, affine transformations, parallel & perspective projections, and lighting.

**CS 169 -- Programming Languages**

**General Departmental Goals and Objectives:** 3a

Specific Goals and Objectives: In this course, students will be exposed to
a variety of programming languages, in addition to studying the theoretical
foundations for programming languages. This course helps students overcome
fears and aversions to learning additional programming languages.
Among the various topics presented, students will

- learn about classifications of programming languages (e.g., procedural, functional, logic, imperative) and learn an example from different paradigms.
- examine the differences in languages in terms of availability of data types, program structures, variable bindings, parameter passing schemes, and other aspects.
- study an overview of formal language and automata theory to learn about the abstract background for programming languages.
- learn about issues raised by parallel computing and languages and languages structures needed for parallel programming.

Specific Goals and Objectives: In this courses, students will learn and demonstrate an understanding of the development of significant areas of the development of mathematics, with emphasis on the concepts of number, limit, the role of geometry and the development of mathematical rigor.

Students will learn to express mathematical ideas and proofs with correctness, precision, and clarity. This will include careful attention to the interplay of geometry, algebra, and numerical argument in their writing and proofs.

Specific Goals and Objectives: The students should learn

- first, how to understand and state the relevant parts of a given problem;
- second, how to find a connection between the given data and the mathematics that may be used to find the problem's solution and then make a plan for obtaining the solution;
- third, carry out the plan;
- fourth, examine the solution to see if it makes sense, if its correctness can be verified, if the ideas used can help you to solve similar more complicated problems, if you could have done the problem in an easier way, etc.

**Math 174 -- Differential Geometry**

**General Departmental Goals and Objectives:** 2b

Specific goals and objectives: Through this course, students will

- Develop and demonstrate the ability to apply techniques from calculus to prove statements about curves and surfaces.
- Acquire knowledge of the fundamental vocabulary of curvature for one- and two-dimensional objects in three-space.
- Practice and demonstrate mastery of techniques and theories of analysis and geometry.

Specific goals and objectives: This course will strengthen each student's

- ability to use theory to solve concrete problems
- write proofs
- understand applications of abstract algebra
- know the theory behind the mathematics used for cryptography
- solve recreational problems, many of which are rooted in number theory.

- enable students to see the beauty of number theory
- learn the history and basics concepts of number theory
- give students the ability to solve problems in elementary number theory.

Specific Goals and Objectives: Students should demonstrate, by the end of the course, that they know some of the uses of, and how to solve, problems involving:

- permutations
- combinations
- generating functions
- recursion relations
- (PIE) the principal of inclusion exclusion
- (PET) the Pólya Enumeration Theorem
- a selection of topics from combinatorial geometry
- graph enumeration
- algebraic combinatorics.

Specific Goals and Objectives: In this course, students will learn to:

- Appreciate and develop facility with mathematical structures. We will connect the different representations and properties of graphs and develop facility in their use in algorithms. We will learn to write graph-theoretic proofs by studying existing proofs and writing our own. We will understand the place of graph theory in the larger structure of discrete mathematics.
- Understand the foundations of Computer Science and appreciate some of its theoretical and applied uses. We will learn ways to represent graphs as data structures, and develop graph algorithms for classical problems in graph theory. We will become adept at applying these algorithms and proving their correctness.

Specific Goals and Objectives: In this course, students will learn

1) symmetric key and public key cryptography, digital signatures, hash functions and certificates and how all of these are incorporated in secure transactions.

2) the history and politics of cryptography and the standards and policies that apply to it.

3) connections between theoretical mathematics and computer science.

4) more about creating and using algorithms.

Specific Goals and Objectives: In this course, students will learn

1) major industrial, military and private applications of cryptography, including time stamping, Kerberos, PGP, key management, quantum cryptography, secret sharing, electronic elections, and digital cash.

2) how to analyze the running time of encryption, decryption and cryptanalysis.

3) to implement major cryptographic algorithms.

4) to combine problem solving abilities with programming in a quarter-long project.

Specific Goals and Objectives: By the end of this course, students be able to

1) understand and implement basic techniques of digital image processing, and

2) understand and implement basic watermarking and steganography techniques.

This page last updated 21 May 2014.