MATH 478
On Expressing Numbers
Spring 2016
Division III
Quantitative/Formal Reasoning
This is not the current course catalog
Class Details
The real numbers are overall mysterious. Attempts even to describe different real numbers can quickly lead to deep, open questions in mathematics. For example, writing numbers via their decimal expansions leads to the result that a number is rational precisely when the decimal expansion is eventually periodic. There is an entirely different method for describing real numbers: continued fractions, which go back thousands of years. Here every real number can be captured by a sequence of integers (just like for the decimal expansion) but now eventually periodicity corresponds to the number being a square root. The mathematics of continued fractions, and especially their higher dimensional generalizations, lead to a great deal of mathematics. We will be using tools from linear algebra, functional analysis, dynamical systems, ergodic theory and algebraic number theory to explore the best way to express a real number.
The Class:
Format: lecture
Limit: none
Expected: 15
Class#: 3180
Grading: yes pass/fail option, yes fifth course option
Limit: none
Expected: 15
Class#: 3180
Grading: yes pass/fail option, yes fifth course option
Requirements/Evaluation:
exams and homework
Prerequisites:
MATH 350 or MATH 351, and MATH 355
Enrollment Preferences:
Seniors
Distributions:
Division III
Quantitative/Formal Reasoning
Class Grid
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HEADERS
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CLASSESColumn header 2DREQColumn header 3INSTRUCTORSColumn header 4TIMESColumn header 5CLASS#
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MATH 478 - 01 (S) LEC On Expressing Numbers
MATH 478 - 01 (S) LEC On Expressing NumbersDivision III Quantitative/Formal ReasoningMWF 10:00 am - 10:50 am
Chemistry 2063180
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