COURSE UNIT TITLE

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

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

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

Face to face and presentation

Assessment Methods

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

Contribution of Learning Outcomes to Programme Outcomes