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Course Criteria
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1.00 Credits
s essential for majors in biology, chemistry, computer science, mathematics, physics, and environmental science and policy. Part I includes functions, limits, continuity, differentiation of algebraic and trigonometric functions, mean-value theorem and various applications. Part II includes Riemann sums and integrals, techniques and applications of integration, improper integrals, transcendental functions (logarithms, exponential functions and inverse trigonometric functions). Part III includes further topics from calculus proper (sequences, series, polar coordinates) and introduces linear algebra (vectors, matrices and linear systems). Though not all results are derived rigorously, care is taken to distinguish intuitive arguments from rigorous proofs. MATH 120, MATH 121 and 122 fulfill the formal-analysis requirement. MATH 122 is a prerequisite for MATH 131 for students who have taken MATH 120, MATH 121.
Prerequisite:
Prerequisite for Math 120: appropriate score on the mathematics placement test or passing grade in MATH 119.
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1.00 Credits
See MATH 120.
Prerequisite:
A passing grade in Math 121.
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1.00 Credits
Two-course sequence for strong students with interest in mathematics, computer science, physics, and other natural sciences. Physics majors usually take MATH 124 simultaneously with PHYS 120 and MATH 125 simultaneously with PHYS 121. Previous experience with calculus is recommended but not required. The honors calculus sequence covers much the same topics from calculus as the regular sequence (MATH 120, MATH 121, MATH 122 ), but takes two semesters instead of three, and emphasizes both mathematical rigor and physical intuition. MATH 124 and MATH 125 fulfill the formal-analysis requirement.
Prerequisite:
Prerequisite for MATH 124: an appropriate score on the mathematics placement test.
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1.00 Credits
A requirement for mathematics and physics majors; highly recommended for all computer-science majors. Topics include systems of linear equations and their solutions, matrices and matrix algebra, inverse matrices; determinants and permutations; real n-dimensional vector spaces, abstract vector spaces and their axioms, linear transformations; inner products (dot products), orthogonality, cross products, and their geometric applications; subspaces, linear independence, bases for vector spaces, dimension, matrix rank; eigenvectors, eigenvalues, matrix diagonalization. Some applications of linear algebra will be discussed, such as computer graphics, Kirchoff's laws, linear regression (least squares), Fourier series, or differential equations.
Prerequisite:
MATH 121 or MATH 125.
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1.00 Credits
Modern analysis provides a language and unifying framework for theories encountered throughout mathematics. In this course, students learn to understand, formulate and prove mathematical statements. Ideas first encountered in calculus—convergence, completeness and integration—are studied in depth. Other topics include metric spaces, normed spaces, compactness and measure theory (Lebesgue integration). Required for mathematics majors by the junior year, and earlier if possible.
Prerequisite:
MATH 122 or MATH 125.
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1.00 Credits
Designed for undergraduate science and mathematics majors. Includes Cauchy's theorem, power series, Laurent series, the residue theorem, harmonic functions and physical applications, such as problems in two-dimensional flow. An introduction to Riemann surfaces if time permits.
Prerequisite:
MATH 131 and MATH 172.
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1.00 Credits
An introduction to probability theory and mathematical statistics that emphasizes the probabilistic foundations required to understand probability models and statistical methods. Topics covered will include the probability axioms, basic combinatorics, random variables and their probability distributions, mathematical expectation and common families of probability distributions.
Prerequisite:
MATH 121 or MATH 125.
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1.00 Credits
In the 19th century, Kummer introduced “ideal numbers” to salvage unique factorization of integers into primes (which breaks down in some rings of algebraic integers). This course discusses unique factorization and the modern theory of rings and their ideals, emphasizing Euclidean domains. Other algebraic structures (groups, fields) also are introduced. Required for all mathematics majors.
Prerequisite:
MATH 130.
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1.00 Credits
This course is designed to encourage students to consider how business is embedded into the larger society. It will introduce students to basic management skills and the context in which they are applied. Whether a person is working in a complex organization, such as a bank, university, high-tech firm, hospital or manufacturer; participating in a student-run activity; volunteering for a local nonprofit; or working a summer job—management skills are necessary. For management majors and minors, the course provides an introduction to the topics they will study in greater depth in their future course work. For students not majoring in management, it provides an opportunity to learn basic skills that will be helpful in their current and future activities in organizations. The course structure includes readings, lecture, service learning, case analyses, role plays and experiential exercises. The course involves considerable interaction between the professor and students, and among students, because the practice of management is about people working with, listening to, and respecting people who have different backgrounds, experiences and opinions. This class fulfills the Verbal Expression requirement.
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1.00 Credits
Presents the theory and techniques of financial accounting. Teaches students an understanding of accounting information, as a basis for financial statement analysis and decision making, and the environment in which it is developed and used. The course structure includes readings, lecture, discussions, and problem solving. Topics include accrual basis accounting, transaction analysis, accounting cycle, and preparation and analysis of financial statements (income statement, balance sheet, and statement of cash flows) for service, merchandising and manufacturing companies.
Prerequisite:
This course is not recommended for students to take during their first semester at Clark.
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