COURSE UNIT TITLE

: TECHNICAL ENGLISH II

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
ELECTIVE

Offered By

Mathematics

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSOCIATE PROFESSOR BURCU SILINDIR YANTIR

Offered to

Mathematics (Evening)
Mathematics

Course Objective

This course aims to lead you think mathematically using elementary number theory accompanied with its history and essays on history of mathematics, and also to write beautiful mathematics.

Learning Outcomes of the Course Unit

1   be able to describe the methods of proof
2   be able to define mathematical terms
3   be able to develop and present mathematical arguments with appropriate notation and structure
4   be able to apply mathematical induction
5   be able to think rigorously
6   be able to write the development of mathematics through its history

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Algebraic properties of the number systems: natural numbers, integers, rational numbers, real numbers and complex numbers.
2 Quadratic polynomials, completing the square and conic sections: parabola, ellipse, hyperbola.
3 Axiomatic construction of the real number system and positive integers, integers and rational numbers obtained from the axioms of the real number system.
4 Induction. Many examples for induction. Miscellenous exercises for real numbers involving induction. Cauchy-Schwarz Inequality and Arithmetic-Geometric Mean Inequality.
5 Eratosthenes construction of the Earth size. Various proofs of Pythagorean Theorem. Pythagorean triples.
6 Definitions, Theorems and Proofs. Techniques of proof: direct method, proof by cases, proof by contradiction, induction and more sophisticated induction techniques, contrapositive method. Some common mistakes.
7 Divisibility and the Sieve of Eratosthenes. Division algorithm. Euclidean algorithm to find the greatest commond divisor and to find integers s,t that satisfies gcd(a,b)=as+bt. Solution of linear congruences. Solution of linear equations ax+by=c in integers.
8 Midterm Exam
9 Prime numbers. Prime divisibility. Factorization and the Fundamental Theorem of Arithmetic. The greatest common divisor gcd(a,b) and the least common multiple lcm(a,b).
10 Modular arithmetic. Properties of congruences.
11 Complex numbers. Construction of complex numbers using the real number system, polar form of complex numbers, De Moivre s Theorem, n-th roots of complex numbers, roots of unity in complex numbers, The Fundamental Theorem of Algebra.
12 More topics for proofs in elementary number theory: Fermat s Little Theorem and Euler s Formula, Euler s Phi Function, the Chinese Remainder Theorem, prime numbers, counting primes, Mersenne Primes, perfect numbers.
13 Powers modulo m and successive squaring; computing k-th roots modulo m; powers, roots and unbreakable codes.
14 More topics for proofs in elementary algebra. The ring of integers modulo n. Rings, integral domains and fields. The group of units in the ring of integers modulo n and orders of its elements. Groups and orders of its elements. Using Lagrange's Theorem for groups to prove Euler-Fermat formula and Fermat's Little Theorem.

Recomended or Required Reading

Textbooks:

[1] Houston, K. How to Think like a Mathematician, A Companion to Undergraduate Mathematics. Cambridge,
2009. [Turkish translation: Matematikc i gibi Du s u nmek, Lisans Matematig i ic in bir Kılavuz, c evirenler
Mehmet Terziler ve Tahsin O ner, Palme Yayıncılık, 2010.]

[2] Silverman, J. H. A Friendly Introduction to Number Theory. Pearson, 2012.

[3] Rotman, J. J. A Journey into Mathematics, An Introduction to Proofs. Dover, 2007.

[4] Higham, N.J. Handbook of Writing for the Mathematical Sciences. Second edition. SIAM, 1997.

[5] Vivaldi, F. Mathematical Writing, An Undergraduate Course. The University of London, 2011.

[6] Tanton, J. Encyclopedia of Mathematics. Facts on File, 2005.

[7] The history of Mathematics archive: http://www-history.mcs.st-and.ac.uk/index.html

[8] Darling, D. The Universal Book of Mathematics,From Abracadabra to Zeno's Paradoxes, John Wiley and Sons, 2004.

Planned Learning Activities and Teaching Methods

Face to face and presentation

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 MTE 1 MIDTERM EXAM 1
2 MTE 2 MIDTERM EXAM 2
3 FIN FINAL EXAM
4 FCG FINAL COURSE GRADE MTE1 * 0.30 + MTE2 * 0.30 + FIN * 0.40
5 RST RESIT
6 FCGR FINAL COURSE GRADE (RESIT) MTE1 * 0.30 + MTE2 * 0.30 + RST * 0.40


*** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

English

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

e-mail: engin.mermut@deu.edu.tr
Phone: (232) 30 18582

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 13 3 39
Preparation for midterm exam 2 12 24
Preparation for final exam 1 13 13
Preparations before/after weekly lectures 12 2 24
Final 1 3 3
Midterm 2 3 6
TOTAL WORKLOAD (hours) 109

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13
LO.145
LO.243353
LO.334433433
LO.4344334433
LO.534433453
LO.6435

CONTACT INFORMATION
Dokuz Eylül Üniversitesi Cumhuriyet Bulvarı No: 144 35210 Alsancak / İZMİR
Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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