Core B2 Problem Solving

MATH1041

Lecturer : Norbert Peyerimhoff

Term : Michaelmas 2013/14

Lectures :
  • Mondays, 14:00-15:00 in PH8

Office hour : Mondays 11:00-12:00, CM320



Seminars :

  • Group 6: Mondays, 9:00-10:00 in CM105 (weeks 2,4,6,8,10), Prof. N. Peyerimhoff

  • Group 6: Mondays, 9:00-11:00 in CM105 (weeks 3,5,7,9), Prof. N. Peyerimhoff

  • Group 1: Tuesdays, 16:00-17:00 in CM105 (weeks 2,4,6,8,10), Dr. O. Post

  • Group 1: Tuesdays, 16:00-18:00 in CM105 (weeks 3,5,7,9), Dr. O. Post

  • Group 4: Wednesdays, 9:00-10:00 in CM105 (weeks 2,4,6,8,10), Prof. J. Hunton

  • Group 4: Wednesdays, 9:00-11:00 in CM105 (weeks 3,5,7,9), Prof. J. Hunton

  • Group 9: Wednesdays, 9:00-10:00 in CM219 (weeks 2,4,6,8,10), Prof. N. Peyerimhoff

  • Group 9: Wednesdays, 9:00-11:00 in CM219 (weeks 3,5,7,9), Prof. N. Peyerimhoff

  • Group 2: Thursdays, 9:00-10:00 in CM105 (weeks 2,4,6,8,10), Prof. S. F. Ross

  • Group 2: Thursdays, 9:00-11:00 in CM105 (weeks 3,5,7,9), Prof. S. F. Ross

  • Group 3: Thursdays, 9:00-10:00 in CM219 (weeks 2,4,6,8,10), Dr. D. Wirosoetisno

  • Group 3: Thursdays, 9:00-11:00 in CM219 (weeks 3,5,7,9), Dr. D. Wirosoetisno

  • Group 5: Thursdays, 11:00-12:00 in CM105 (weeks 2,4,6,8,10), Dr. D. J. Smith

  • Group 5: Thursdays, 11:00-13:00 in CM105 (weeks 3,5,7,9), Dr. D. J. Smith

  • Group 7: Thursdays, 14:00-15:00 in CM105 (weeks 2,4,6,8,10), Dr. O. Hryniv

  • Group 7: Thursdays, 14:00-16:00 in CM105 (weeks 3,5,7,9), Dr. O. Hryniv

  • Group 8: Fridays, 14:00-15:00 in CM219 (weeks 2,4,6,8,10), Dr. P. S. Craig

  • Group 8: Fridays, 14:00-16:00 in CM219 (weeks 3,5,7,9), Dr. P. S. Craig

Content of Lectures

Date Content pdf-file
Monday, 7 October 2013 (Week 1) Mathematical statements and connectives (and, or, not, implies), truth tables, equivalent statements, De Morgan's Rule pdf-file
Monday, 14 October 2013 (Week 2) The "if and only if" connective, basic set notation and number sets, Venn Diagrams, equality of sets and subsets pdf-file
Monday, 21 October 2013 (Week 3) Mathematical structuring (definitions, theorems, proof, ...), writing of a proper mathematical text illustrated by an example from Euclidean Geometry pdf-file
Monday, 28 October 2013 (Week 4) Open statements, quantifiers, order of quantifiers matters, negation of statements with quantifiers, infinite unions and intersections, De Morgan for infinite unions and intersections of sets pdf-file
Monday, 4 November 2013 (Week 5) Correct negation of ''If A then B'', Indirect Proof, Induction and Strong Induction pdf-file
Monday, 11 November 2013 (Week 6) Contrapositive statements, Contrapositive proof technique and examples, necessary and sufficient conditions, injective, surjective and bijective pdf-file
Monday, 18 November 2013 (Week 7) Modelling problems and their three stages (modelling stage, solution stage, and looking back stage), Overhanging Domino Problem as a concrete example pdf-file
Monday, 25 November 2013 (Week 8) Cardinality of a set, comparison of sizes of finite and infinite sets, Cantor-Bernstein-Schroeder Theorem, countability and uncountable sets, cardinalities of sets of rational and irrational numbers, cardinality of the power set pdf-file
Monday, 2 December 2013 (Week 9) Preimage and image of a set under a map, examples, equivalence relations, equivalence classes, representatives, examples pdf-file
Monday, 9 December 2013 (Week 10) Discussion of certain aspects of the first two assessments pdf-file



Problem Sheets 		Date Sheets Solutions
Week 1 (7.10-11.10) Logic Problems pdf Logic Solutions pdf
Week 2 (14.10-18.10) Set Problems pdf Set Solutions pdf
Week 3 (21.10-25.10) Writing Maths Problems pdf Writing Maths Solutions pdf
Week 4 (28.10-1.11) More Logic and Sets Problems pdf More Logic and Sets Solutions pdf
Week 5 (4.11-8.11) Proof Problems pdf Solutions pdf
Week 6 (11.11-15.11) Formulate mathematical conditions pdf Solutions pdf
Week 7 (18.11-23.11) Modelling problems pdf Solutions pdf
Week 8 (25.11-29.11) Number Problems pdf Solutions pdf
Week 9 (2.12-6.12) Preimages and Equivalence Relations pdf Solutions pdf
Week 10 (9.12-13.12) Potpourri of Problems pdf Solutions pdf

Assessment : The schedule is tentative and may change in due course. There will be 3 summative assessments during the term (contributing in total 40% to the final mark of the whole module).

  • First assessment (take home): Set on Monday, 21 October, 15:00

    This assessment will contribute 30% to the final mark of this part of the module (i.e., it will contribute 12% to the whole module).

  • Second assessment (take home): Set on Monday, 4 November, 15:00

    This assessment will contribute 30% to the final mark of this part of the module (i.e., it will contribute 12% to the whole module). Feedback about mistakes will be given after each try.

  • Third assessment (take home): Set on Monday, 25 November, 15:00

    This assessment will contribute 40% to the final mark of this part of the module (i.e., it will contribute 16% to the whole module).

VERY IMPORTANT for take home assessments: Students must not use books, internet or other sources (other than the books listed in the Literature below) when dealing with these assessments and working on them, nor seek help from other people (e.g., fellow students or their tutors). Assessed work must be their own authentic work, and this needs to be confirmed by them with their signature! Otherwise no mark will be given to their work.

Literature

Much of what you will do is based on the following highly recommendable book.
  • Kevin Houston, How to think like a mathematician, Cambridge University Press, 2009, ISBN 9780521719780

Further useful books are:
  • George Polya, How to solve it, Penguin 1990 ISBN 9870140124996
  • Alan F. Beardon, Creative Mathematics, Cambridge University Press, 2009, ISBN 9780521130592
  • Martin Day, An Introduction to Proofs and the Mathematical Vernacular, downloadable book at http://www.math.vt.edu/people/day/ProofsBook/
  • John Mason, Leone Burton and Kaye Stacey, Thinking Mathematically, Addison Wesley 1985 ISBN 0201102382


Last modified: 3.10.2013