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Unit of study_

Algebra and Logic (MATH3066)

This unit of study unifies and extends mathematical ideas and techniques that most participants will have met in their first and second years, and will be of general interest to all students of pure and applied mathematics. It combines algebra and logic to present and answer a number of related questions of fundamental importance in the development of mathematics, from ancient to modern times. Classical and novel arithmetics are introduced, unified and described abstractly using field and ring axioms and the language of field extensions. Applications are presented, in particular the unsolvability of the celebrated classical construction problems of the Greeks. Quotient rings are introduced, culminating in a construction of the real numbers, by factoring out rings of Cauchy sequences of rationals by the ideal of null sequences. Axiomatics are placed in the context of reasoning within first order logic and set theory. The Propositional and Predicate Calculi are studied as model axiomatic systems in their own right, including sketches of proofs of consistency and completeness. The final part of the course introduces precise notions of computability and decidability, through abstract Turing machines, culminating in the unsolvability of the Halting Problem and the undecidability of First Order Logic.

Classes
Three 1 hour lectures and one 1 hour tutorial per week.

Assessment
One 2 hour exam (60%), two assignments (15% each), peer review of each assignment (5% each).

Pre-requisites

6 credit points of Intermediate Mathematics

Prohibitions

MATH3062 or MATH3065

Details

Semester 1

05 Mar 2018

Department/School: Mathematics and Statistics Academic Operations
Study Mode: Normal (lecture/lab/tutorial) day
Census Date: 31 Mar 2018
Unit of study level: Senior
Credit points: 6.0
EFTSL: 0.125
Available for study abroad and exchange: Yes
Faculty/department permission required? No
Location
Census dates shows the latest date to cancel out of a unit*
HECS Band: 2
Courses that offer this unit

Non-award/non-degree study If you wish to undertake one or more units of study (subjects) for your own interest but not towards a degree, you may enrol in single units as a non-award student. Cross-institutional study If you are from another Australian tertiary institution you may be permitted to undertake cross-institutional study in one or more units of study at the University of Sydney.

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