The final examination for MATH 135 in Winter 2012 is Tuesday, April 17 from 0900–1130. All sections except the Dubai section write in Sections 1–5 of the PAC. For students in Dubai, please contact

Prof. Harmsworth regarding arrangements.

Final Examination Coverage

1. The final examination covers all course material with a weighting towards material covered after the midterm. 2. About 25% of the examination is based on calculation. The remainder is based on proof.

3. No calculators are permitted.

Studying

1. Start early.

2. Make a list of all definitions. Be able to state all of the definitions. Definitions covered in the text by Solow but not in class are not required.

3. Make a list of all propositions that were given an acronym. Be able to state all of the propositions.

4. For examples of problems involving calculation, prepare representative problems for sets, truth tables, computing gcds, finding certificates for gcds, solving linear Diophantine equations, solving linear and polynomial congruences, solving simultaneous linear congruences, determining prime factorizations and computing gcds using prime factorizations, arithmetic with complex numbers, Cartesian and polar forms of complex numbers, finding n-th roots, polynomial factorization, binomial coefficients and the Binomial Theorem.

5. Analyze proofs done in class or on the assignments. Can you identify why and where each proof technique was used? Can you identify where each part of the hypothesis was used?

6. Do proofs. Where can you find practice propositions? The proofs done in class, the exercises found in many chapters of the course notes, the problems and further examples at the end of some of the chapters of the course notes, the problems in the Practice, Practice, Practice chapters of the course notes, the Written Assignments, the Electronic Assignments, the midterms and final examinations posted at the MathSoc exam bank http://mathsoc.uwaterloo.ca/, problems from the reference book (Gilbert and Vanstone’s Mathematical Thinking) and problems created in study groups are all sources of propositions. You are not expected to reproduce the RSA Theorem, the Characterization of Pythagorean Triples or Fermat’s Last Theorem (n = 4). However, you are expected to understand the proofs and be able to complete parts of the proof with some guidance.

MapleTA has had additional quizzes added to practice your computational skills.

Before The Final Examination

1. Get enough sleep.

2. Arrive on time.

3. Arrive at the right place.

4. Bring your Watcard. We use it to confirm your identification and make sure that you can legitimately write this exam.

5. Bring extra pens, pencils and erasers. Most students write in pencil so that they can erase