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Analysis I, Spring 2006

(Complete Item Description)

Abstract:: Analysis I covers Fundamentals of Mathematical Analysis: Convergence of Sequences and Series, Continuity, Differentiability, Riemann Integral, Sequences and Series of Functions, Uniformity, Interchange of Limit Operations. Three versions of the course are available. Each option shows the utility of abstract concepts and teaches understanding and construction of proofs. Option A chooses less abstract definitions and proofs, and gives applications where possible. Option B is more demanding and is for students with more mathematical maturity; it places more emphasis on Point-Set Topology and N-Space, whereas Option A is concerned primarily with the Real Line. Option C is a variant of Option B, with further instruction and practice in written and oral communication.

Subject:: Mathematics and Statistics
Grade Level:: Post-secondary
Collection:: MIT OpenCourseWare

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The Function Integral and Area

(Complete Item Description)

Abstract:: Introduction to a fundamental principle of integral calculus- the area of a function.

Subject:: Mathematics and Statistics
Grade Level:: Post-secondary
Collection:: Connexions

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Math Help Pages - Calculus Index - Technical Tutoring

(Complete Item Description)

Abstract:: This site features a menu of lessons and reference material on calculus concepts. Featured are several definitions of the derivative, treatments of discontinuity, and discussion of logarithms, integration, and antiderivatives. The sections are presented with clear notation and examples.

Subject:: Mathematics and Statistics
Grade Level:: Secondary, Post-secondary
Collection:: NAGT Cutting Edge (SERC)

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The Prime Number Theorem (PNT)

(Complete Item Description)

Abstract:: The Prime Number Theorem is of key interest to number theorists owing to the importance of Riemann's work on the subject.
But it can also be viewed as a fitting function that approximates the distribution of the prime numbers. We provide such a "pedestrian" viewpoint and development using elementary mathematics.

Subject:: Science and Technology
Grade Level:: Post-secondary
Collection:: Connexions

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Riemann Area Optimization and Histogram Construction

(Complete Item Description)

Abstract:: The purpose of this module is to assist histogram design. The module presents an integral in terms of the Riemann sum equation for finding the area of a data-set. It builds on an associative technique (from a discrete to continuous function) suggested by the sub-interval in the delta-x and bin number in the histogram. The resulting area spectrum contains possible areas and an actual area for a data-set. The module concludes with statements on the possible optimization of the integral by calculating the actual area. Building a histogram in this way may imply compression qualities for variance in the data-set frequency distribution.

Subject:: Mathematics and Statistics
Grade Level:: Post-secondary
Collection:: Connexions

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