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
MAT 1012 TECHNICAL ENGLISH II COMPULSORY 3 0 0 4

Offered By

Mathematics

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSISTANT PROFESSOR CELAL CEM SARIOĞLU

Offered to

Mathematics (Evening)
Mathematics

Course Objective

This aim of this course is to read, write, argue, speak fluently in mathematics when solving problems. Our main aim is problem solving, really interesting mathematical problems. Of course, we cannot do this in vacuum; so we shall study some of the following interesting elementary topics which you shall always use in your mathematics education: Elementary number theory, Complex numbers, Limits of sequences of real numbers. We shall always emphasize writing mathematics rigorously with a correct English. Besides, the topics we shall study are also fundamental and interesting topics, and it is very important for you to learn them rigorously in a detailed way. We expect from you to understand these interesting topics but our emphasis will be on writing and explaining well in mathematics so as to show a clear understanding of the concepts and a clear thinking. If you understand something really, then you must be able to know how to explain it. This course will help you by producing practice in writing, arguing, talking for some interesting and fundamental topics in mathematics. Writing well and explaining your arguments clearly is what is required in every course in our department. Mathematically, you must learn how to write rigorously and clearly proofs using the techniques of proof: direct method, proof by cases, proof by contradiction, induction and more sophisticated induction techniques, proof by contrapositive method.

Learning Outcomes of the Course Unit

1   be able to use the techniques of proof.
2   be able to identify and use precise definition of mathematical terms.
3   be able to develop and present mathematical arguments with appropriate notation and structure.
4   be able to use the concepts devoloped in elementary number theory, complex numbers and limits of sequences of real numbers.
5   be able to think and write rigorously.
6   be able to make and write computations in elementary number theory, complex numbers and limits of sequences of real numbers.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Number Theory, Pythagorean Triples and the Unit Circle.
2 Divisibility and the Greatest Common Divisor.
3 Linear Equations and the Greatest Common Divisor.
4 Factorization and the Fundamental Theorem of Arithmetic.
5 Congruences, Powers, Fermat's Little Theorem, Euler's Formula.
6 Euler's Phi Function and the Chinese Remainder Theorem.
7 Prime Numbers, Counting Primes, Mersenne Primes, Perfect Numbers.
8 Powers Modulo m and Successive Squaring. Computing kth Roots Modulo m. Powers
9 Roots, and Unbreakable Codes.
10 Complex numbers, its construction using the real number system, polar form of complex numbers.
11 De Moivre s Theorem, n-th roots of complex numbers, roots of unity in complex numbers, The Fundamental Theorem of Algebra.
12 Limits of sequences of real numbers: Axioms for the Real Number System, Completeness of R. Convergence and divergence of sequences of real numbers. Limits of convergent sequences of real numbers. Monotone Convergence Theorem and completeness of the real number system (the least upper bound property of R).
13 Sum, product and quotient of sequences, and further important theorems for sequences.
14 Subsequences. Nested Interval Theorem. Bolzano-Weierstrass Theorem. Cauchy sequences.

Recomended or Required Reading

Textbooks:

[1] Silverman, J. H. A Friendly Introduction to Number Theory. 4th edition. New international edition.
Pearson, 2014:
web page of the book by the author: http://www.math.brown.edu/~jhs/frint.html
web page of the author: http://www.math.brown.edu/~jhs/

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

[3] Kane, J. M. Writing Proofs in Analysis. Springer, 2016.

[4] Krantz, S. G. Techniques of Problem Solving. AMS, 1997.

[5] Phillips, G. M. Mathematics is not a Spectator Sport. Springer, 2005.

[6] Farin, G. and Hansford, D. Practical Linear Algebra, A Geometry Toolbox. 4th edition. CRC Press, 2022.

[7] Houston, K. How to Think like a Mathematician, A Companion to Undergraduate Mathematics. Cambridge,
2009. [Turkish translation: Matematikçi gibi Düşünmek, Lisans Matematiği için bir Kılavuz, çevirenler
Mehmet Terziler ve Tahsin Öner, Palme Yayıncılık, 2010.]
web page of the book by the author: http://www.kevinhouston.net/httlam.html
web page of the author which also contains some talks and videos:
http://www.kevinhouston.net/index.html
DVD records of three talks on a workshop for Teaching Students to Write Mathematics:
http://www.kevinhouston.net/dvds/writing-math.html

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

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

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

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

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

Planned Learning Activities and Teaching Methods

Lecture notes, presentation, problem solving, discussion.

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 VZ Vize
2 FN Final
3 BNS BNS VZ * 0.40 + FN * 0.60
4 BUT Bütünleme Notu
5 BBN Bütünleme Sonu Başarı Notu VZ * 0.40 + BUT * 0.60


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

Further Notes About Assessment Methods

None

Assessment Criteria

%40 (Midterm examination) +%60 (Final examination)

Language of Instruction

English

Course Policies and Rules

The student is responsible for attending 70% of the courses throughout the semester. Action will be taken within the framework of the relevant regulations regarding unethical behavior that may occur in classes and exams. You can obtain the DEU Faculty of Science teaching and exam practice principles regulation from http://web.deu.edu.tr/fen

Contact Details for the Lecturer(s)

Asst. Prof. Dr. Celal Cem SARIOĞLU
E-mail: celalcem.sarioglu@deu.edu.tr
Phone: +90 232 301 8585
Office: B212 (Mathematics Department)

Office Hours

To be announced later.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 14 3 42
Preparation for midterm exam 1 15 15
Preparation for final exam 1 20 20
Preparations before/after weekly lectures 13 2 26
Final 1 2 2
Midterm 1 2 2
TOTAL WORKLOAD (hours) 107

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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