618-150 Number, Shape and Choice

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Objectives:

On completion of this subject students should:

Comprehend:

• some fundamental concepts in mathematics, both old and new;

• the value of well-chosen notation and terminology;

• the notion of a mathematical model;

• the concept of a logical, mathematical argument.

Have developed:

• the ability to use a simple mathematical model incorporating the ideas of number, shape, and choice;

• the ability to construct simple, logical arguments and draw conclusions;

• the ability to write a brief, clear account of a simple mathematical concept or a simple mathematical model.

Appreciate:

• the beauty of mathematics;

• the usefulness of mathematics.

Content:

Basic themes in non-calculus based mathematics and selected applications, chosen from the following topics. Number: The natural numbers, primes, divisors, congruences, applications to cryptography. Rational and irrational numbers. Countability. Powers and roots, algebraic equations, famous impossibilities, musical scales. Shape: Geometric similarity and scaling. Self-similarity and fractals. Classical and modern geometries and applications. Symmetries and tilings. Chaos: Calculator experiments, iteration, iterated mappings, geometrical notion of convergence, period-doubling and chaos. Choice: Competitive and cooperative games, linear programming, optimal decision making and voting systems.

Assessment: