MPS Course Goals
Last Updated 9/27/08, CCS + 9/29SRS
Math 105, Contemporary Mathematics:
Contemporary Mathematics is a very general title. This course was added several years ago to
give students an additional elective that:
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requires relatively little mathematics background
allows flexibility in the selection of topics
gives students who made an effort a positive experience with mathematics
is useful for students in education
This course does not
1. prepare students for another math class in a sequence or
2. teach a particular body of mathematics such as algebra, trigonometry, or statistics.
After offering this course several times we found that the selection of topics is important and
they should be both interesting and accessible.
Math 109, Elementary Functions:
Elementary Functions is designed for a student who has had three years of high school
mathematics but who is not prepared for calculus. The course should
1. solidify the student's knowledge of algebra and
2. extend it to include an understanding of general functions, graphing, and specific functions
such as the log and exponential functions.
The course does not cover trigonometric functions. However, a tutorial in trigonometry (Math
190) is available.
Math 111, Calculus I:
This is an introduction to calculus with focus on functions, limits, derivatives, and applications
of derivatives. It seeks
1. to review the notions of function, inverse function, exponential function, and log function
2. to develop students' understanding of the importance of limits as the principal ingredient in
calculus
3. to introduce students to derivatives and applications
Math 112, Calculus II:
Calculus II finishes the introduction to calculus with the notions of integration, the Fundamental
Theorem of Calculus, and applications, and then continues to introduce related topics such as
differential equations, partial derivatives, and vectors. While the course is preparation for
Calculus III, it is also designed to cover important topics for those students who will not continue
the calculus sequence. In particular, students will
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1. understand the meaning of "definite integral" in general and in important examples
2. see the relationship between differentiation and integration and apply it to problems
3. learn what a differential equation and a solution are and appreciate their ubiquity in nature
and in mathematics
4. understand vector arithmetic, the equivalence of mathematical and physical notions of
"vectors," and applications to representations of lines and planes
5. learn about partial derivatives, their basic properties, and their basic interpretation
Math 151, Elementary Statistics:
1. Learn how data can inform us about the world, focusing on
o the techniques of data analysis
o summarizing and interpreting batches of data with the aid of graphical and/or
conceptual models,
o ideas important in collecting data as in designing experiments and sampling, and
o the ideas and techniques of statistical inference--drawing conclusions from a set of
data about the world it came from.
2. Vocabulary, concepts, and techniques of statistical analysis.
3. A critical approach to published statistical information.
Outcomes: homework and exam exercises utilizing mostly real world examples from the
textbook and current publications.
Math 211, Calculus III:
Students learn about sequences and series of numbers and functions, then study multivariable
calculus—vector functions, functions of severable variables, and generalizations of the
Fundamental Theorem of Calculus. The course leads to
Objectives
1. understanding of the computational and conceptual aspects of sequences and series, in
particular the meanings limits and real numbers
2. ability to calculate and to understand basic properties of vector functions and curves in space
3. appreciation of the geometry of functions of several variables, in particular the meanings of
maxima and minima
4. understanding of the geometric and calculational significance of Stokes's and Gauss's
Theorems
Outcomes
Students should be able to:
1. Determine if various infinite sums converge and, in some cases, what they converge to
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2. Approximate various values and functions, within given tolerances, using more easily
computed values and functions
3. Apply techniques of differential and integral calculus to curves and surfaces in multiple
dimensions
4. Frame real-world problems (i.e. planetary motion) as problems in appropriate-dimensional
calculus and find solutions (i.e. Kepler's laws) using (3)
Math 195, Tutorial in Trigonometry:
Math 212, Linear Algebra:
1. learn the basic terminology and methods of linear algebra
2. cover representative applications of linear algebra
3. learn about mathematical structures and proofs
Math 213, Ordinary Differential Equations and Applications:
This course introduces the practical and theoretical aspects of ordinary differential equations. In
particular, students will
1. understand the quantitative and qualitative meanings of differential equations and their
solutions, especially in applied examples
2. learn standard techniques for finding analytic solutions
3. estimate solutions and evaluate their qualitative nature even when an exact analytic
solution is unavailable
4. develop the theory of differential equations, including first order systems and their
relationship to equations of arbitrary order
Math 251, Probability and Statistics I:
Similar to Math 151, but mathematical competence through Calculus I is assumed. Additional
goals include
1. understand the probability that underpins the normal distribution
2. classical inference
Outcomes: Homework, take home exams and in class quizzes; joint project in data analysis from
independently found or generated data.
Math 267, Discrete Mathematics I:
1. learn the terminology and techniques of some key areas of discrete mathematics
2. gain mathematical and logical experience and sophistication
3. learn to understand and do proofs
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Math 300, Probability and Statistics II:
Math 301, Applied and Computational Mathematics:
1. Master the numerical methods to solve mathematical problems
2. Evaluate the applicability, reliability and efficiency of algorithmic processes
3. Model real world problems using procedural mathematical algorithms
Math 305, Operations Research:
Objectives:
1. Apply operations research methods to a variety of decision-making settings.
2. Understand the implications of the results of an analysis using these methods.
3. Be able to communicate technical issues orally and in writing.
Outcomes
1. Abilty to formulate problems as linear programs, solve them using the simplex method, and
interpret the results using sensitivity analysis.
2. Abilty to formulate problems as dynamic programs, solve them using dynamic programming,
and interpret results.
3. Ability to recognize, formulate, and solve network problems using techniques such as
shortest route, minimal spanning tree, and PERT/CPM.
4. Ability to present the results of an analysis orally and in writing.
How measured:
1. Students present the results of their readings and/or analyses in class.
2. Students complete projects and/or problems that require them to identify and apply methods
presented in the course.
Math 312, Real Analysis:
This course has the multiple purposes of filling in the theoretical underpinnings of calculus and
emphasizing the importance of proof as a tenet of mathematics generally, while beginning the
study of analysis as a subject in its own right. Students will
1. develop a better understanding of the nuances of real numbers
2. learn and use basic topological notions on the real line and in abstract metric spaces
3. master the technical definitions and proofs concerning continuity, differentiability, and
integrability of functions of a single variable, as demonstrated in the use of the techniques
for investigating related problems and constructing similar proofs
Math 313, Abstract Algebra:
Another "theory course," Abstract Algebra emphasizes the importance of proof in mathematics
as well as introduces students to the basic objects of algebra. Students
1. understand the definitions and basic properties of groups, rings, and fields in the abstract and
in common examples such as integers, rational numbers, real numbers, and matrices
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2. discover the still more abstract concepts of object, subobject, quotient object, isomorphism,
and their relationships, and learn to use them as unifying notions that apply to many algebraic
objects
Math 290/390, Internship in Mathematics:
CS 105, HTML:
The objective of CS 105 is to learn to develop web pages in HTML (hypertext markup
language). Specific goals are
1. knowledge of HTML syntax,
2. the ability to use HTML in a realistic application, and
3. the ability to continue to explore HTML as an independent learner.
CS 108, Excel:
The objective of CS 108 is to learn to develop and work with Excel spreadsheets. Specific goals
are
1. knowledge of Excel syntax,
2. the ability to use Excel in a realistic application, and
3. the ability to continue to explore Excel as an independent learner.
CS 109, Access:
The objective of CS 109 is to learn to develop web pages in Access databases. Specific goals are
1. knowledge of Access syntax,
2. the ability to use access in a realistic application, and
3. the ability to continue to explore Access as an independent learner.
CS 131, Computer Programming 1:
Goal:
1. Learn to solve problems and implement the solutions in the C++ programming language
using methods that lead to correct, usable, readable, and modifiable programs.
Outcomes
:
1. Knowledge of C++ syntax for basic data and control structures.
2. The ability to translate a problem statement to an algorithm, program it in C++, and test for
correctness
How measured:
1. Weekly programs.
2. Exams that test knowledge of syntax and programming techniques.
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CS 132, Computer Programming 2:
A continuation of CS 132 with emphasis on data structures.
Goals:
1. knowledge of representative data structures, including stacks, queues, trees, and linked lists.
2. the ability to represent them in C++ classes
3. the ability to use object-oriented methods and classes to organize programs of medium
complexity.
CS 225:
1. Understand the Von Neumann machine concept and information representation.
2. Sensitivity to the primitive sequential/jump nature of the computer, underlying higher-level
language programming; how higher level programming structures can be compiled to a
representative assembly language.
3. Awareness of issues of time and space at the machine level, including operating system
program management and memory allocation schemes.
4. Strength the habits of clear organization and documentation of a project and the resulting
program.
5. Strengthen step-by-step tracing debugging skills.
substantial exercises in assembly language level programming, and a group project: without the
“safety net” of a language with built-in encapsulation.
CS 310, Software Engineering:
1. understand the software development cycle for implementing a large system
2. understand the methodology and models to translate a desired system to a formal
requirements specification
3. understand the methodology and models to translate a formal requirements specification to a
system design
CS 325, Database Systems:
Goals
1. Understand and appreciate the principles of database design.
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Outcomes
:
1. The student is able to translate user requirements into a semantic model
2. The student is able to translate a semantic model into a relational model
3. The student is able to implement, manage, and exploit the relational model using SQL.
How measured:
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1. A project
CS 330, Internet Architecture and Programming:
CS 330 explores the architectures and programming languages that support communicating and
computing over a network. Specific goals include understanding of
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JavaScript for client side-programming
PHP for server-side programming
the ability to interface with a server-side database
the OSI and TCP/IP reference models
the specific protocols and capabilities at each level of the TCP/IP reference model
CS 340, Unix/Linux Systems Administration
1. Understand the role and responsibilities of a Unix system administrator
2. Grasp the nuts and bolts for Unix/Linux system administration
3. Develop an appreciation of technical documentation
CS 368, Discrete Math II:
Continuation of Math 267.
1. Continue developing ability to reason mathematically and practice proving, building on
Math.
2. Introduce mathematical concepts, models and structures especially pertinent to computer
science.
CS 290/390, Internships in Computer Science:
Physics 106, Introductory Astronomy:
Physics 111L, Fundamentals of Physics I:
1. Understand the basic concepts and laws of classical Newtonian mechanics
2. Apply the mechanics to real world physical and engineering problems
3. Equip students with the background and reasoning ability for other science courses
Physics 212L, Fundamentals of Physics II:
1. Understand the more advanced concepts and laws of classical mechanics and
thermodynamics
2. Apply to real world physical and engineering problems
3. Equip students with the background and reasoning ability for other science courses
Physics 213L, Fundamentals of Physics III:
1. Understand the concepts and laws of Electromagnetism and optics
2. Apply to real world physical and engineering problems
3. Equip students with the background and reasoning ability for other science courses
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Physics 221L, Principles of Electronics:
Physics 302, Introduction to Modern Physics:
1. Understand the concepts and laws of modern physics
2. Apply to real world physical and engineering problems
3. Equip students with the background and reasoning ability for other science courses
4. Appreciate the brainstorming works of the 20th century pioneering physicists.
Physics 303, Theoretical Mechanics:
The course seeks to expand students' understanding of Newton's Laws from various perspectives.
Specifically, students will
1. learn to apply the Laws thoroughly in three or more spatial dimensions using a variety of
coordinate systems
2. discover the utility and significance of the Lagrangian formulation of mechanics
3. study a variety of particular physical phenomena, including oscillations, gravitation and
orbits, and coupled systems
Physics 307, Quantum Mechanics and Relativity:
Physics 340, Experimental Physics:
Physics 290/390, Internships in Physics:
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