MATH1041

**Lecturer :** Norbert Peyerimhoff

**Term :** Michaelmas 2013/14

- 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).

**Literature**

- 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