[Santa Clara University]
Department of Mathematics
and Computer Science

Santa Clara University
Department of Mathematics and Computer Science

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.

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.

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.
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.


Core Curriculum Learning Goals and Objectives for Mathematics Courses (primarily for Math 6, 7, 11, 30). 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.


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.
(Abbreviations: DG = Department Goal, CG = Core Goal) CS 3 -- Introduction to Computing and Applications
General Departmental Goals and Objectives: 1a; 3a,b

Math 4 (formerly 41 before Summer 2009) -- The Nature of Mathematics

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

Math 7 -- Calculus for Social Science
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.


Math 8 -- Introduction to Statistics
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 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:
Math 9 -- Precalculus
General Departmental Goals and Objectives: 1a; 2b
NOTE: This course is designed to be taken only by those who need to review high school mathematics in order to take Business or Science/Engineering Calculus courses. It does not satisfy any university core curriculum requirement. (Humanities students who wish to fulfill a "mathematics" core curriculum requirement should consider taking Math 41 (4).)
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.

Math 12 -- Calculus and Analytic Geometry II
General Departmental Goals and Objectives: 1a; 2b
Specific Goals and Objectives: In this course, focusing on integral calculus, Math 13 -- Calculus and Analytic Geometry III
General Departmental Goals and Objectives: 1a; 2b
Specific Goals and Objectives: In this course, focusing on topics in discrete mathematics, Math 14 (formerly 21 before Summer 2009) -- Calculus and Analytic Geometry IV

Math 21 (renumbered 14 after Summer 2009) -- Calculus and Analytic Geometry IV
General Departmental Goals and Objectives: 1a; 2b
Specific Goals and Objectives: In this course, focusing on calculus concepts applied to surfaces in 3-dimensions on other calculus concepts, Math 22 -- Differential Equations
General Departmental Goals and Objectives: 1a; 2b
Specific Goals and Objectives: In this course, students
Math 30 -- Calculus for Business 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 particularly applicable to the world of business and to explain their reasoning.

Math 31 -- Calculus for Business II
General Departmental Goals and Objectives: 1a; 2b
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.

Math 32 -- Mathematical Logic
General Departmental Goals and Objectives: 1a; 2a

Math 41 (renumbered 4 after Summer 2009) -- The Nature of Mathematics
General Departmental Goals and Objectives: 1a; 2a; 2b
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:


Math 45 -- Mathematics for Elementary Teachers II
General Departmental Goals and Objectives: 1a; 2a; 3b
Specific Goals and Objectives: In this course, students will:
Math 51/COEN 19 -- Discrete Mathematics
General Departmental Goals and Objectives: 1a; 2a; 3b
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: In addition to learning these various concepts which are useful in their own right, students will achieve our overarching goal: they will be able to read mathematical arguments written by others and they will be able to produce their own proper mathematical arguments -- not only on the primary topics listed above (and others that we will cover in the course), but also on other topics that the students will come upon in the future.

Math 52 -- Introduction to Abstract Algebra
General Departmental Goals and Objectives: 2a; 2b; 3b
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:


CS 60 -- Object Oriented Programming
General Departmental Goals and Objectives: 3a; 3b
Specific Course Goals and Objectives: In this course, students will be able to

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


Math/CS 90 -- Lower Division Seminars
General Departmental Goals and Objectives: 1a; 2b

Math 100 -- Writing in the Mathematical Sciences
General Departmental Goals and Objectives: 2a; 2b
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
Math 101 -- A Survey of Geometry
General Departmental Goals and Objectives: 2b
Specific goals and objectives: Through this course, students will
Math 102 -- Advanced Calculus
General Departmental Goals and Objectives: 2a; 2b
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.

Math 103 -- Linear Algebra II
General Departmental Goals and Objectives: 2b; 3b
Specific Goals and Objectives: In this course, students will synthesize related mathematical objects such as matrices, polynomials, and n-tuples, and practice and demonstrate mastery of proofs and problem-solving in ways that emphasize the unity of concepts and arguments. Students will practice and demonstrate mastery of axiomatic reasoning, especially as applied to the architecture of vector spaces and linear transformtions between them.

Math 105 -- Theory of Functions of a Complex Variable
General Departmental Goals and Objectives: 2b; 3b
Specific Goals and Objectives: In this course, students will learn how to

Math 111 -- Abstract Algebra I
General Departmental Goals and Objectives: 2a; 2b
Specific Goals and Objectives: In this course, students will be expected to Beyond these subject-specific skills, students will improve their aptitute for analyzing arguments and identifying the assumptions upon which they are formed.

Math 112 -- Abstract Algebra II
General Departmental Goals and Objectives: 2a; 2b
Specific Goals and Objectives: In this course, students will be expected to Beyond these subject-specific skills, students will improve their aptitute for analyzing arguments and identifying the assumptions upon which they are formed.

Math 113 -- Topology
General Departmental Goals and Objectives: 2a; 2b
Specific Goals and Objectives: In this course, students will be expected to
Math 122 -- Probability and Statistics I
General Departmental Goals and Objectives: 1a; 2b
Specific Goals and Objectives: In this course, students will be expected to
Math 123 -- Probability and Statistics II
General Departmental Goals and Objectives: 1a; 2b; 3b
Specific Goals and Objectives: In this course, students will be expected to
Math 125 -- Mathematical Finance
General Departmental Goals and Objectives: 1a; 2b
Specific Goals and Objectives: In this course, students will be expected to
Math 133 -- Logic and Foundations
General Departmental Goals and Objectives: 2a

Math 134 -- Set Theory
General Departmental Goals and Objectives: 2a

Math 144 -- Partial Differential Equations
General Departmental Goals and Objectives: 1a; 2b; 3a; 3b
Specific Course Goals and Objectives: In this course, students will be expected to:
Math 153 -- Intermediate Analysis I
General Departmental Goals and Objectives: 2a

Math 154 -- Intermediate Analysis II
General Departmental Goals and Objectives: 2a

Math 155 -- Ordinary Differential Equations
General Departmental Goals and Objectives: 1a; 2b; 3b
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


CS 162 -- Theory of Automata and Languages II
General Departmental Goals and Objectives: 2a; 3a; 3b

CS 163/COEN 179 -- Theory of Algorithms
General Departmental Goals and Objectives: 3b
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.

CS 164 -- Computer Simulation
General Departmental Goals and Objectives: 1a; 3a; 3b
Specific Goals and Objectives: By the end of this course, students will be able to: Math/CS 165 -- Linear Programming
General Departmental Goals and Objectives: 2b; 3b
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.
Math/CS 166 -- Numerical Analysis
General Departmental Goals and Objectives: 1a; 2b; 3a; 3b
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
CS 167 -- Switching Theory and Boolean Algebra
General Departmental Goals and Objectives: 3a

CS 168 -- Computer Graphics
General Departmental Goals and Objectives: 1a; 3a; 3b
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


Math 170 -- Development of Mathematics
General Departmental Goals and Objectives: 2a; 2b
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.

Math 172 -- Problem Solving
General Departmental Goals and Objectives: 2b; 3b
Specific Goals and Objectives: The students should learn Induction and analogy, along with other mathematical techniques, will be emphasized throughout the course, and studied in various contexts, so that students will be encouraged to "think outside the box."

Math 174 -- Differential Geometry
General Departmental Goals and Objectives: 2b
Specific goals and objectives: Through this course, students will


Math 175 -- Theory of Numbers
General Departmental Goals and Objectives: 2a; 2b; 3b
Specific goals and objectives: This course will strengthen each student's This course will
Math 176 -- Combinatorics
General Departmental Goals and Objectives: 2b; 3b
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:
Math 177 -- Graph Theory
General Departmental Goals and Objectives: 2a; 2b; 3b
Specific Goals and Objectives: In this course, students will learn to: Math 178 -- Cryptography
General Departmental Goals and Objectives: 1a; 2b; 3b
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.

CS 181 -- Applied Cryptography
General Departmental Goals and Objectives: 3a; 3b
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.

CS 182 -- Digital Steganography
General Departmental Goals and Objectives: 3a; 3b
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.

Math/CS 190 -- Upper-Division Seminars
General Departmental Goals and Objectives: 2a; 2b; 3a; 3b (as appropriate)

Math/CS 196 -- Advanced Topics
General Departmental Goals and Objectives: 2a; 2b; 3a; 3b (as appropriate)

Math/CS 198 -- Internship/Practicum
General Departmental Goals and Objectives: 2a; 2b; 3a; 3b (as appropriate)

Math/CS 199 -- Independent Study
General Departmental Goals and Objectives: 2a; 2b; 3a; 3b (as appropriate)


This page last updated 30 March 2013.