Elementary track mathematics

Elements of Number Theory

Lecturer: Dr. Hnan Haider 

Course type: Lecture + exercise, required, 2 weekly-hour, Semester

The purpose of the course is to provide students with knowledge of the fundamentals of number theory and the natural numbers set and skills for finding the greatest common divisor and solving Diophantine equations. The course is designed to expose them to concepts such as natural numbers, prime numbers, common denominator, least common multiple, and more, as well as give them high-level skills in solving mathematical problems and expose them to problems and challenges that have occupied the mathematical world throughout the history of mathematics, and even to unsolved problems in number theory. As part of the course, students will be exposed to interesting mathematical theorems and their proofs, such as Euler’s theorem, the Chinese remainder theorem, and more.

Final grade components: submission of 3 exercises 15%, final exam 80%

Plane  Geometry 

Lecturer: Dr. Loai Abdullah

Course type: Lecture + exercise, required, 2 weekly hrs., Semester

The purpose of the course is to introduce students to fundamental concepts in palatial geometry, such as segments, congruent and similar triangles, squares, circles, and proportions in a triangle, as well as the exact formulations of definitions and statements in the field of geometry. It is designed to develop awareness and understanding of accurate proofs built on a set of axioms, to foster the ability to construct a topic based on a set of concepts and axioms, and to provide examples of non-Euclidean geometries.

Final grade components: tests 20%, final exam 80%

Spatial Geometry

Lecturer: Dr. Loai Abdullah

Course type: Lecture + exercise, required, 2 weekly hrs., Semester

The purpose of the course is to expose students to fundamental concepts in spatial geometry: sphere, cube, cylinder, pyramid, and more, to develop their spatial sense and the layout of three-dimensional bodies. The course is also designed to introduce them to precise formulations of spatial geometry definitions and statements and to cultivate their skills in constructing a topic based on a set of concepts and axioms. The course will also address other complex bodies, using the concepts of volume, surface area, and shell area.

Final grade components: tests 20%, final exam 80% 

Graphs and Functions 

Lecturer: Dr. Mohammad Abu Hamed

Course type: Lecture + exercise, required, 2 weekly hrs., Semester

The course deals with the concept of function, families of functions and their algebraic and graphical properties, and the relationship between them. Its purpose is to introduce students to linear, rational, exponential, polynomial, rational, trigonometric, and more functions. In each function family, emphasis will be placed on the intersection with the axes, areas of increase and decrease, even and odd, positive and negative, vertical and horizontal asymptotes, extreme points, and graphical description. Students will also be exposed to the uses of functions in everyday life and to solving word problems with the help of functions.

Final grade components: exercises 15%, final exam 85%

Analytical Geometry 

Lecturer: Dr. Abed Elhalim Abed Elfatah

Course type: Lecture + exercise, required, 2 weekly hrs., Semester

The course deals with applying algebraic ways to solve geometry problems and familiarity with special geometric loci and their properties. The course will cover, among other things, the distance between two points, the midpoint of a line segment and dividing a segment in a given ratio, calculating the area of a triangle using its vertices, a line in a plane (equation and different forms of the equation, parallel and perpendicular lines), the angle between two lines, distance between two lines, the median formula, perpendicular, angle bisector, bisector in a triangle, the equation of the circle and the relative position of two circles or tangent line to a circle, the equation of the ellipse and the tangent line to the ellipse, the equation of the hyperbola and asymptotes and tangent line to the hyperbola, the equation of the parabola and the tangent line to the parabola, and conic sections.

Final grade components:  test 20%, exercises 20%, final exam 60%

Probability and Combinatorics 

Lecturer: Dr. Fathi Saleh 

Course type: Lecture + exercise, required, 2 weekly hrs., Semester

The purpose of the course is to expose students to the basics of Counting Theory and Combinatorics and their use in problem-solving and to introduce them to the basics of probability theory and the probabilistic tools needed for statistical work. A variety of topics will be discussed, including the addition and multiplication principles, permutations and substitutions, inclusion–exclusion principle, random experiment, probability as a limiting relative frequency, probability space, conditional probability, Bayes’ theorem, the law of total probability, pairwise and mutually independent events, Bernoulli trial, random variables, probability function of a random variable, typical discrete random variables (binomial, geometric, Poissonian), expectation and variance of random variables, and expectation of a random variable (binomial, geometric and Poisson).

Final grade components: active participation in solving exercises 10%, test 20%, final exam 70%.

Logic and Sets

Lecturer: Dr. Wafiq Hibi

Course type: Lecture + exercise, required, 2 weekly hrs., Semester

The purpose of the course is to provide students with basic knowledge of mathematical logic and set theory and an in-depth introduction to the concept of infinity and to develop their mathematical thinking through set theory. Students will learn mathematical language and logic, as well as how to deal with the proof of mathematical theorems using mathematical logic. 

Among other things, the course will cover the following content: mathematical statements (statement counting, truth table, and equivalent statements), the concept of sets (equivalence, inclusion, belonging, complements, and examples of important sets), De Morgan’s laws, set operations (union, intersection, difference, Cartesian product), power of a finite set, power finite sets union, relations (equivalence relations, partial and total order relations), functions (injective function, superfunction, function composition, and the inverse function), as well as cardinals and equivalences between sets and countable sets.

Final grade components: midterm 30%, final exam 70%.

Introduction to Algebra

Lecturer: Dr. Ghalib Nassar

Course type: Lecture + exercise, required, 2 weekly hrs., Semester

The purpose of the course is to strengthen and expand the algebraic technique. It is also designed to introduce students to concepts, theorems, and calculation methods in the fields of linear algebra, including equalities and inequalities with absolute value, mathematical induction, complex numbers, fields and subfields, systems of linear equations, vectors, matrices, determinants, Cramer’s rule, vector spaces, and subspaces. These will serve as a basis for more advanced topics in the field of algebraic structures.

Final grade components: exercises 20%, midterm 20%, final exam 60%.

Introduction to Geometry

Lecturer: Dr. Hnan Haider

Course type: Lecture + exercise, required, 2 weekly hrs., Semester

The course is designed to expose students to basic concepts in the field of geometry: types of lines, types of angles, triangles, squares, polygons, circles, measurements, symmetry, perimeter and area, tessellation, three-dimensional shapes and their layout, volumes, shell and surface area, the five platonic solids and isometric mapping. Emphasis will be placed on developing an understanding of the logical and mathematical characteristics of geometry, the development of geometric intuition and spatial vision, as well as on deepening familiarity with the new curriculum for geometry teaching (recognizing mistakes, difficulties, and misconceptions among students and imparting skills of utilizing high thinking levels while performing assignments).

Final grade components: classroom presentation 40%, final paper 60%.

Algebraic structures

Lecturer: Dr. Abed Elhalim Abed Elfatah

Course type: Lecture + exercise, required, 2 weekly hrs., Semester

The purpose of the course is to develop tools for understanding abstract concepts in the field of algebra, a familiarization and deepened understanding of the basics of algebra, and the cultivation of abstract thinking and the ability to bridge it with concrete thinking. The course will cover, among others, the topics of the group concept: axioms, examples of groups and group properties, subgroups, functions between groups, sections, and Lagrange’s theorem, normal groups. Basic concepts of fields, homomorphism of circles and ideals, Euclid’s algorithm, characterization of a field, field extension, vector space, polynomial decomposition, and finite fields.

Final grade components: submission of exercises 20%, midterm 20%, final exam 60%.

The Infinity Concept and Analysis

Lecturer: Dr. Mohammad Abu Hamed

Course type: Lecture + exercise, required, 2 weekly hrs., Semester

The course is designed to provide in-depth knowledge of concepts related to functions and series and to train students on how to investigate families of functions and series, their behavior at infinity, the concept of limit, limit calculations, the concept of the derivative, derivatives of elementary functions by definition, in-depth investigation on the behavior of functions at infinity, slant asymptotes, and convergence and divergence of infinite series.

Final grade components: exercises and reading reports 10%, final exam 90%.

Mathematics in Everyday Life

Lecturer: Dr. Wafiq Hibi

Course type: Lecture + exercise, required, 2 weekly hrs., Semester

The course is designed to examine the connection between mathematics and everyday life. It will focus on providing students with tools that will enable them to use basic mathematical principles in everyday life problems, including the application of basic trigonometry of triangles and right-angled triangles to calculate heights of buildings, towers, and mountains; basic astronomical applications such as calculating the volume of planets and their distance from Earth; using a database (diagrams, graphs, verbal text, price list, publications, etc.) as a basis for solving problems with natural numbers, fractions, and percentages; and various mathematical topics related to daily life such as mental calculations, area and volume calculations, unit conversion, ratio and more.

Final grade components: exercises and reading reports 10%, final exam 90%.

Solving Word Problems

Lecturer: Dr. Asad Mahajne 

Course type: Lecture + exercise, required, 2 weekly hrs., Semester

The purpose of the course is to expose students to different types of word problems, their characteristics, different strategies and models for solving word problems, and difficulties and misconceptions that accompany learning and teaching the subject, as well as to train them in creating word problems of different types. The course is also designed to impart skills and strategies for solving one-step, two-step, and multi-step problems, various models and aids for solving word problems, an informed look at the types of problems in textbooks, and handling different kinds of problems.

Final grade components: exercises and reading reports 10%, final exam 90%.

Statistical Data Research

Lecturer: Dr. Abed ElRahman Khalil

Course type: Lecture + exercise, required, 1 weekly-hrs., Semester

The course offers students a review of the basic knowledge of the fundamentals of quantitative research. It refreshes their orientation in descriptive and inferential statistics to provide them with skills for building quantitative research, analyzing it, testing hypotheses, and drawing conclusions. In addition, students will experience designing and analyzing quantitative research layouts. They will experience data collection methods, different research tools, data analysis methods in quantitative research, and especially statistical analysis in SPSS software. 

Among other things, the course will touch on the topics of descriptive and inferential statistics (statistical tests and hypothesis testing); one-way analysis of variance and posthoc tests such as the Tukey-Kramer test and the Chaffey test), and the use of variance analysis in educational research; Regression analysis (simple regression, multiple regression, and the use of multiple regression in educational research); morality, ethics rules, and research evaluation criteria; and writing the findings chapter in a research paper.

Final grade components: final exam 70%, writing an abbreviated research proposal 20%, submission of 3 exercises 10%.