Mathematics Department Course for the academic year (2023-2024).

Note: A short description of each course by the lecturer.

First Semester

First Second Semester (2)

 SecThird Semester (3)

 

SeF Fourth Semester (4)

Fifth Semester (5)

Sixth Semester (6)

Fourth Year Seventh Semester (7)

Eigth Semester (8)

No	Course Code	Course Name	Hours/week	Units
1		Axiomatic System and Geometry	5	5
2		Research Project	4	4
3		Viewing  and Application	4	4

                                                                                            

                                                                                             European Credit Transfer System (ECTS)

First Year/ Fall Semester
Course Code	Course Title	أسماء المواد	ECTS	T	A	P	Prerequisite
MD1S101	Calculus I	التفاضل وا التکامل I	8	6
MD1S102	College Algebra	الجبر للكليات	3	2
MU1S103	Academic Debate	الحوار الاکادیمی	5	2		2
MU1S104	Kurdish Studies	دراسات كوردية	5	3
MU1S105	English Language I	اللغة الانجليزية I	5	3	1
MU1S106	Information Technology	تکنلوجیا المعلومات	4			3
Total			30	16	1	5
Total hours Per Week				22

 

First Year/ Spring Semester
Course Code	Course Title	أسماء المواد	ECTS	T	A	P	Prerequisite
MD1S201	Calculus II	التفاضل واالتکامل II	8	6			MD1S101
MD1S202	Foundation of Mathematics I	اسس الریاضیات  I	4	3
MD1S203	Introduction to Statistics	مقدمة في الإحصاء	5	2		1
MC1S204	General Psychology	علم النفس العام	5	3
MU1S205	English Language II	اللغە الانجلیزیة II	5	3	1		MU1S105
MU1S206	Environmental Conservation (Elective)	حماية البيئة	3	2	1
MU1S207	Social Awareness (Elective)	الوعي الاجتماعي
Total			30	19	2	1
Total hours Per Week				22

 

Second Year/ Fall Semester
Course Code	Course Title	أسماء المواد	ECTS	T	A	P	Prerequisite
MD2S101	Advanced Calculus	التفاضل وا التکامل المتقدم	5	4			MD1S201
MD2S102	Ordinary Differential Equations	المعادلة التفاضلية الاعتيادية	8	6			MD1S201
MD2S103	Computer Programming with MATLAB	برمجة الحاسوب مع ماتلاب	6	2		2
MD2S104	Foundation of Mathematics II	اسس الریاضیات II	6	4			MD1S202
MC2S105	Educational Psychology	علم النفس التربوی	5	3
MU2S106	English (Intermediate)	اللغە الانجلیزیة III		2		1	MU1S205
Total			30	21	0	3
Total hours Per Week				24

 

Second Year/ Spring Semester
Course Code	Course Title	أسماء المواد	ECTS	T	A	P	Prerequisite
MD2S201	Probability Theory	نظرية الاحتمالات	7	5			MC1S203
MD2S202	Linear Algebra	الجبر الخطي	8	6
MD2S203	Computer Progrmming	برمجة الحاسوب	5	2		1
MD2S204	Mathematical Modelling	نموذج رياضي	5	3
MU2S205	English(Academic Writing)	اللغە الانجلیزیەIV		2		1	MU2S106
MC2S206	Development Psychology	علم النفس النمو	5	2		2
Total			30	20	0	4
Total hours Per Week				24

 

Third Year/ Fall Semester
Course Code	Course Title	أسماء المواد	ECTS	T	A	P	Prerequisite
MD3S101	Mathematical Analysis	التحلیل الریاضی	7	5			MD1S201 &MD2S104
MD3S102	Linear Programming	البرمجة الخطية	5	3
MD3S103	Group Theory	نظرية الزمر	5	4
MC3S104	Educational Counseling & Mental Health	الإرشاد التربوي والصحة النفسية	5	3
MC3S105	General Teaching Methods	طرائق التدریس العامة	5	4
MD3S106	Graph Theory	نظرية البيانات	3	2
Total			30	21	0	0
Total hours Per Week				21

 

Third Year/ Spring Semester
Course Code	Course Title	أسماء المواد	ECTS	T	A	P	Prerequisite
MD3S201	Numerical Analysis	التحليل العددي	8	4		2	MD2S103
MD3S202	Ring Theory	نظرية الحلقات	5	3			MD3S103
MD3S203	Number Theory	نظرية الأعداد	4	3			MD2S104
MD3S204	Mathematical Teaching Methodology	طرائق التدریس ریاضیات	5	3			MC3S105
MC3S205	Measurement and Evaluation	القیاس والتقويم	5	2	1
MD3S206	Mathematical textbook Analysis	تحليل الکتاب الریاضي	3	2
Total			30	17	1	2
Total hours Per Week				20

 

Fourth Year/ Fall Semester
Course Code	Course Title	أسماء المواد	ECTS	T	A	P	Prerequisite
MD4S101	Elective	مادة اختيارية	5	3			Dependent on optional
MD4S102	Complex Analysis	التحلیل العقدی	8	6			MD1S201
MD4S103	Geometry	الهندسة	8	6
MC4S104	Educational Management & Supervision	الإدارة والاشراف التربوي	5	3
MU4S105	Research Methodology	منهج البحث	4	2	1
Total			30	20	1	0
Total hours Per Week				21

 

Fourth Year/ Spring Semester
Course Code	Course Title	أسماء المواد	ECTS	T	A	P	Prerequisite
MD4S201	Research Project	بحث  التخرج	10	2		2
MC4S202	Viewing and Application	المشاهدة والتطبيق	20	2		16
Total			30	4	0	18
Total hours Per Week				22

Course Definitions

Fourth year courses

1-Topology: Topology isanimportant andinterestingareaofmathematics,thestudyofwhich will not only introduce you to new concepts and theorems, but also put into context old ones, such as continuous functions. However, to say just this is to understate the significance of topology. It isso fundamental that itsinfluence is evident in almost every other branch of mathematics. Topologyhasseveral different branches—generaltopology (also known as point-settopology), algebraictopology, differentialtopologyandtopological algebra—the first,generaltopology,beingthedoortothestudyoftheothers.

2-Complex Analysis: This course is an introductory course on Complex Analysis. It is designed for students in the disciplines of Mathematics and Physics. It may, however, be useful to students in Engineering and other related fields. It introduces students to the complex numbers system and varieties of operations, analyses and problems that may arise within this context. It also equips students with mathematical techniques and skills to handles such cases.

3-Geometry: The primary goal of this semester is to familiarize students with axiomatic geometry and teach them how to create a model for an axiomatic system and use axioms and undefined terms to prove theorems.

4-Advanced Calculus: Calculus is the study of how things change. It provides a framework for modelling systems in which there is change and a way to deduce the predictions of such models.

5_ Special Methods of Teaching: This subject aims to prepare and familiarize lecturers with methods of teaching which are needed in every teaching sector.

6_ Administration & Educational Supervision: This is to familiarize students with the concepts of administration and supervision in both practical and theorical fields. This is achieved through studying administration and development concepts in relation to general and educational administration and schools. Through discussions of these concepts, prospective lecturers collect all the skills and basic principles needed for successful administration in terms of skills and effectiveness

Third stage Courses:

1-Mathematical analysis: By the end of this module, students should be familiar with the following subjects: real numbers, the density of rational and irrational numbers, sequences of real numbers, convergent sequences, bounded sequences, monotone sequences and Cauchy sequences and the relationship between these types of sequences. In addition, they will have an understanding of metric spaces, open and closed sets, derived sets, compact sets with some important theorems continuity of functions between metric spaces, sequences of functions, Riemann integral, differentiation, measure theory, Lebesgue theory of integration and measurable and integrable functions.

2-Numerical Analysis: This course will emphasize the development of numerical algorithms to provide solutions to common problems formulated in science and engineering. The primary objective of the course is to develop a basic understanding of the construction of numerical algorithms, and, perhaps more importantly, the applicability and limits of their appropriate use. The emphasis of the course will be a thorough study of numerical algorithms to understand the guaranteed accuracy that various methods provide.

3-Abstract Algebra : plays an increasing role in the pure sciences as well as in mathematics. This course is intended to familiarize the student with the basic concepts, axioms, principles and methods of Abstract Algebra. This course is an introductory course that covers the foundations of Abstract Algebra in the context of Set Theory, Group Theory, Ring Theory and Field Theory

4-Scientific Research Methodology: This course will introduce the student to the basic language and ideas of scientific research methodology which are essential for the completion and submission of graduation research by fourth year students in the department of Mathematical Science required as a condition of graduation for obtaining a B.Sc. degree. This unit deals with the concepts of scientific research and research methodology used in research in general and in mathematics in particular. This will provide students with a solid preparation for their BSc graduation projects and further research projects. They will learn how to review critically and evaluate scientific writing, from books to research papers. Students will receive training in writing academic reports in an appropriate style and structure and will learn how to make and deliver oral presentations.

5-Differential Equations: In this module, we describe the main ideas to solve certain differential equations, such as first-order and higher-order linear equations. We use power series methods to solve variable coefficients second-order linear equations. We introduce Laplace transform methods to find solutions to constant coefficients equations.

6- General Teaching Methods: This subject is all about providing lecturers with suitable methods of teaching which are needed in every teaching sector, and also tries to provide an academic teaching environment leading to teachers equipped with knowledge of modern developments in both education and teaching.

7- Optional (Computing): Computing is one of the most important subjects that everybody needs to know about nowadays, especially those who intend to pursue further studies in the future or those who would like to be teachers. Computing is an electronic tool which is crucially needed for the development of each nation.

Second stage Courses:

1-English Language: Our main aim is to help all our students learn as much English as they need for whatever they plan to do when they leave college, whether that means following a course of academic study, or becoming involved in business, or simply for personal use.

2- Elementary Geometry: On completion of this course, students will be able to:

1 Understand the concept of systems, definition, theorem and undefined terms;

2 Understand the properties of systems;

3 Separate the different statements of either proof (methods of proof), disprove or not both;

4 Apply geometric modelling to modern mathematical problems;

5 Understand the historical background of Euclidean and non-Euclidean (finite) geometry and the development of Euclidean geometry.

 

3- Calculus III: In this course, we will begin by covering the basic concepts of vector spaces. Then, we will study the functions of several variables. After that we will give definitions of limit and continuity for several variables. Furthermore, partial derivatives of such functions will be given. At the end of this course, we will present an introduction about multiple integrals with applications.

4-Probability & Statistics: In this course, we will begin by outlining the basic concepts of Statistics Notation, types of data and chart. Then, we will study the mean and types of mean measures of variation. After that, sample space, events, Probability Function, and Conditional Probability. At the end of this course we will discuss Probability Distribution Prerequisites.

5- Linear Algebra: This course aims to introduce the basic ideas and techniques of linear algebra for use in many other lecture courses. The course will also introduce some basic ideas of abstract algebra and techniques of proof which will be useful for future courses in pure mathematics.

6-Computer Programming: The course has two primary goals: (a) To introduce students to simple computer programming for the solution of mathematical problems that typically arise in a variety of engineering and physics disciplines, (b) and to provide students with basic elements of programming using the MATLAB program

Educational Psychology -7

7_ This course focuses on:

1. Students' general knowledge of educational psychology;

2. Learning about educational psychology, its definitions, origins and development;

3. Identifying theories of educational psychology;

4. Learning about terms of educational psychology as well as developing knowledge about basic topics in educational psychology from which students will benefit in their daily and academic lives.

1-Foundations of mathematics: the study of the logical and philosophical basis of mathematics, including whether the axioms of a given system ensure its completeness and its consistency. Because mathematics has served as a model for rational inquiry, it is used extensively in the sciences. Foundational studies have far-reaching consequences for the reliability and extensibility of rational thought itself.

2-Calculus I: In this course, we will begin by outlining the basic concepts of functions and their graphs. Then, we will study the limits and continuity for various functions. After that, differentiation rules will be defined with their applications, such as extreme values of functions, concavity and curve sketching, applied optimization, and Newton’s method. At the end of this course, we will present a brief introduction about integration and their rules, with some applications.

3-Calculus II is the second course involving calculus, after Introduction to Calculus I. This course includes basic rules of integrations with applications. We will also cover sequence and series in this course. Furthermore, polar coordinates and vectors will also be presented in more detail in Calculus II.

4- English Language: Our main aim is to help all our students to learn as much English as they need for whatever they plan to do when they leave college, whether that means pursuing a course of academic study, becoming involved in business or simply for personal use.

5-Elementary Statistics: This course concentrates on the importance and uses of statistical tools needed in different types of research. It includes (1) descriptive statistics that deals with the collection, organization and presentation of data and (2) inferential statistics that deals with the analysis and interpretation of data which is the main focus. This course provides an overview of descriptive and inferential statistics in the behavioral sciences, social sciences, health sciences, and education. It presents the methods and unifying ideas of data analysis, and the usefulness of data analysis; discusses random sampling which is an important idea in statistics and research; presents the central idea of sampling distribution which is an important fact of probability; describes the reasoning of statistical inference which is the cornerstone of this course; and presents methods of inference for various settings, with a strong emphasis on the practical aspects of using these methods.

6_ IT

Computing is one of the most important subjects that everybody needs to know about nowadays, especially those who intend to pursue further studies in the future or those who would like to be a teacher. Computing is an electronic tool which is crucially needed for the development of each nation.

7_ Philosophy and Education Principles: Familiarizing students with the most important types and philosophical reasoning behind each educational system, teaching them how to adapt modern educational systems. Running a workshop entitled “Towards the Bologna Process by the Mathematics Department”. Link to the workshop:

https://www.facebook.com/408152872665380/posts/1321434874670504?s=100008650059936&sfns=mo https://www.facebook.com/408152872665380/posts/1320306324783359?s=100008650059936&sfns=mo