Seminar in Abstract Mathematics 2009


Lecture Notes (incomplete)

I. The beginning: sets

12:00-14:00 Donderdag, 12 Maart 2009, Kamer 1057, Afdeling Wiskunde, Dept. Wisk. Wetenskappe, Van Der Sterrgebou, Universiteit Stellenbosch

12:00-14:00 Thursday, 12 March 2009, Room 1057, Mathematics Division, Dep. of Math. Sciences, Van Der Sterr Building, Stellenbosch University

II. Functions as sets

13:00-15:00 Vrydag, 20 Maart 2009, Kamer 1057, Afdeling Wiskunde, Dept. Wisk. Wetenskappe, Van Der Sterrgebou, Universiteit Stellenbosch

13:00-15:00 Friday, 20 March 2009, Room 1057, Mathematics Division, Dep. of Math. Sciences, Van Der Sterr Building, Stellenbosch University

III. Properties of the empty set

13:00-15:00 Vrydag, 27 Maart 2009, Kamer 1057, Afdeling Wiskunde, Dept. Wisk. Wetenskappe, Van Der Sterrgebou, Universiteit Stellenbosch

13:00-15:00 Friday, 27 March 2009, Room 1057, Mathematics Division, Dep. of Math. Sciences, Van Der Sterr Building, Stellenbosch University

IV. Composition of relations

13:00-15:00 Vrydag, 17 April 2009, Kamer 1057, Afdeling Wiskunde, Dept. Wisk. Wetenskappe, Van Der Sterrgebou, Universiteit Stellenbosch

13:00-15:00 Friday, 17 April 2009, Room 1057, Mathematics Division, Dep. of Math. Sciences, Van Der Sterr Building, Stellenbosch University

V. The paradox in naive set theory

13:00-15:00 Vrydag, 24 April 2009, Kamer 1057, Afdeling Wiskunde, Dept. Wisk. Wetenskappe, Van Der Sterrgebou, Universiteit Stellenbosch

13:00-15:00 Friday, 24 April 2009, Room 1057, Mathematics Division, Dep. of Math. Sciences, Van Der Sterr Building, Stellenbosch University

VI. Injections and surjections

13:00-15:00 Vrydag, 8 Mei 2009, Kamer 1057, Afdeling Wiskunde, Dept. Wisk. Wetenskappe, Van Der Sterrgebou, Universiteit Stellenbosch

13:00-15:00 Friday, 8 May 2009, Room 1057, Mathematics Division, Dep. of Math. Sciences, Van Der Sterr Building, Stellenbosch University

VII. Set-theoretical approach to the first five postulates of Euclid's geometry

13:00-15:00 Vrydag, 15 Mei 2009, Kamer 1057, Afdeling Wiskunde, Dept. Wisk. Wetenskappe, Van Der Sterrgebou, Universiteit Stellenbosch

13:00-15:00 Friday, 15 May 2009, Room 1057, Mathematics Division, Dep. of Math. Sciences, Van Der Sterr Building, Stellenbosch University


WINTER BREAK


VIII. The meaning of "If A then B"

13:00-15:00 Vrydag, 24 Julie 2009, Kamer 1053, Afdeling Wiskunde, Dept. Wisk. Wetenskappe, Van Der Sterrgebou, Universiteit Stellenbosch

13:00-15:00 Friday, 24 July 2009, Room 1053, Mathematics Division, Dep. of Math. Sciences, Van Der Sterr Building, Stellenbosch University

IX. Natural numbers as a partition of the collection of finite sets

13:00-14:00 Maandag, 27 Julie 2009, Kamer 1053, Afdeling Wiskunde, Dept. Wisk. Wetenskappe, Van Der Sterrgebou, Universiteit Stellenbosch

13:00-14:00 Monday, 27 July 2009, Room 1053, Mathematics Division, Dep. of Math. Sciences, Van Der Sterr Building, Stellenbosch University

X. Discovring the notion of an equivalence relation

13:00-14:00 Vrydag, 31 Julie 2009, Kamer 1053, Afdeling Wiskunde, Dept. Wisk. Wetenskappe, Van Der Sterrgebou, Universiteit Stellenbosch

13:00-14:00 Friday, 31 July 2009, Room 1053, Mathematics Division, Dep. of Math. Sciences, Van Der Sterr Building, Stellenbosch University

XI. Producing partitions out of equivalence relations

13:00-14:00 Maandag, 3/08/2009, Kamer 1053, Afdeling Wiskunde, Dept. Wisk. Wetenskappe, Van Der Sterrgebou, Universiteit Stellenbosch

13:00-14:00 Monday, 3/08/2009, Room 1053, Mathematics Division, Dep. of Math. Sciences, Van Der Sterr Building, Stellenbosch University

XII. Producing equivalence relations out of partitions. Constructing integers

13:00-14:00 Vrydag, 7/08/2009, Kamer 1053, Afdeling Wiskunde, Dept. Wisk. Wetenskappe, Van Der Sterrgebou, Universiteit Stellenbosch

13:00-14:00 Friday, 7/08/2009, Room 1053, Mathematics Division, Dep. of Math. Sciences, Van Der Sterr Building, Stellenbosch University

XIII. Producing partitions out of equivalence relations. Constructing Rational numbers

13:00-14:00 Vrydag, 14/08/2009, Kamer 1053, Afdeling Wiskunde, Dept. Wisk. Wetenskappe, Van Der Sterrgebou, Universiteit Stellenbosch

13:00-14:00 Friday, 14/08/2009, Room 1053, Mathematics Division, Dep. of Math. Sciences, Van Der Sterr Building, Stellenbosch University

XIV. Cardinal (meta)numbers

13:00-14:00 Maandag, 17/08/2009, Kamer 1053, Afdeling Wiskunde, Dept. Wisk. Wetenskappe, Van Der Sterrgebou, Universiteit Stellenbosch

13:00-14:00 Monday, 17/08/2009, Room 1053, Mathematics Division, Dep. of Math. Sciences, Van Der Sterr Building, Stellenbosch University

XV. Counting an infinity

13:00-15:00 Vrydag, 21/08/2009, Kamer 1053, Afdeling Wiskunde, Dept. Wisk. Wetenskappe, Van Der Sterrgebou, Universiteit Stellenbosch

13:00-15:00 Friday, 21/08/2009, Room 1053, Mathematics Division, Dep. of Math. Sciences, Van Der Sterr Building, Stellenbosch University

XVI. Revision: constructing natural numbers, integers and rational numbers

13:00-14:00 Maandag, 24/08/2009, Kamer 1053, Afdeling Wiskunde, Dept. Wisk. Wetenskappe, Van Der Sterrgebou, Universiteit Stellenbosch

13:00-14:00 Monday, 24/08/2009, Room 1053, Mathematics Division, Dep. of Math. Sciences, Van Der Sterr Building, Stellenbosch University

XVII. Cardinal Arithmetic

13:00-15:00 Vrydag, 28/08/2009, Kamer 1053, Afdeling Wiskunde, Dept. Wisk. Wetenskappe, Van Der Sterrgebou, Universiteit Stellenbosch

13:00-15:00 Friday, 28/08/2009, Room 1053, Mathematics Division, Dep. of Math. Sciences, Van Der Sterr Building, Stellenbosch University


SHORT BREAK


XVIII. Cardinal Arithmetic, continued

13:00-14:00 Maandag, 14/09/2009, Kamer 1053, Afdeling Wiskunde, Dept. Wisk. Wetenskappe, Van Der Sterrgebou, Universiteit Stellenbosch

13:00-14:00 Monday, 14/09/2009, Room 1053, Mathematics Division, Dep. of Math. Sciences, Van Der Sterr Building, Stellenbosch University

XIX. The refined definition of Natural Numbers and proof of the Mathematical Induction. Proof by induction that n+1 is not less than n (which is equivalent to the so called "Pigeon Hole Principle")

13:00-14:00 Vrydag, 18/09/2009, Kamer 1053, Afdeling Wiskunde, Dept. Wisk. Wetenskappe, Van Der Sterrgebou, Universiteit Stellenbosch

13:00-14:00 Friday, 18/09/2009, Room 1053, Mathematics Division, Dep. of Math. Sciences, Van Der Sterr Building, Stellenbosch University

XX. The refined definition of Natural Numbers and proof of the Mathematical Induction. Proof by induction that the sum of two natural numbers is a natural number

13:00-14:00 Maandag, 21/09/2009, Kamer 1053, Afdeling Wiskunde, Dept. Wisk. Wetenskappe, Van Der Sterrgebou, Universiteit Stellenbosch

13:00-14:00 Monday, 21/09/2009, Room 1053, Mathematics Division, Dep. of Math. Sciences, Van Der Sterr Building, Stellenbosch University


SHORT BREAK


XXI. Proof by induction that the product of two natural numbers is a natural number. Revisiting the construction of the set of positive rational numbers

13:00-14:00 Maandag, 5/10/2009, Kamer 1053, Afdeling Wiskunde, Dept. Wisk. Wetenskappe, Van Der Sterrgebou, Universiteit Stellenbosch

13:00-14:00 Monday, 5/10/2009, Room 1053, Mathematics Division, Dep. of Math. Sciences, Van Der Sterr Building, Stellenbosch University

XXII. Cancellation laws for natural numbers

13:00-14:00 Maandag, 12/10/2009, Kamer 1053, Afdeling Wiskunde, Dept. Wisk. Wetenskappe, Van Der Sterrgebou, Universiteit Stellenbosch

13:00-14:00 Monday, 12/10/2009, Room 1053, Mathematics Division, Dep. of Math. Sciences, Van Der Sterr Building, Stellenbosch University

XXIII. Natural numbers as a monoid of words made from a single character

13:00-14:00 Vrydag, 16/10/2009, Kamer 1053, Afdeling Wiskunde, Dept. Wisk. Wetenskappe, Van Der Sterrgebou, Universiteit Stellenbosch

13:00-14:00 Friday, 16/10/2009, Room 1053, Mathematics Division, Dep. of Math. Sciences, Van Der Sterr Building, Stellenbosch University

XXIV

13:00-14:00 Maandag, 19/10/2009, Kamer 1053, Afdeling Wiskunde, Dept. Wisk. Wetenskappe, Van Der Sterrgebou, Universiteit Stellenbosch

13:00-14:00 Monday, 19/10/2009, Room 1053, Mathematics Division, Dep. of Math. Sciences, Van Der Sterr Building, Stellenbosch University

XXV

13:00-14:00 Vrydag, 23/10/2009, Kamer 1053, Afdeling Wiskunde, Dept. Wisk. Wetenskappe, Van Der Sterrgebou, Universiteit Stellenbosch

13:00-14:00 Friday, 23/10/2009, Room 1053, Mathematics Division, Dep. of Math. Sciences, Van Der Sterr Building, Stellenbosch University


Organized by

Dr K T Howell
Dr Z Janelidze

Lectures by

Dr Z Janelidze

Student members of the seminar group in 2009

Mr E Alant,
Mr B Carswell,
Mr W Cloete,
Mr S Daniso,
Ms C van Heerden,
Mr M Lambrechts,
Mr Z Madikazi,
Mr R R M Mahomane,
Ms M McLeod,
Mr F I Michael,
Me E Nel,
Mr N Poets,
Mr R M P Prenter,
Mnr A Roos,
Mr T J van Rooyen,
Mr S Swarts,
Mr H L Uys,
Mr J Weideman