Course Description

Preliminary topics which are studied in high school, number theory, inequalities and solution of quadratic and cubic equations, inequalities and finding the solution sets of inequities, set theory and basic set operations, functions and properties and its graphs, absolute value function, linear and quadratic functions, trigonometric functions and their graphs.

Some pre-algebraic and pre-calculus contents and their terminologies, some expression that are used in pure and applied mathematics with their terminology. Writing and reading in math and some grammar of mathematics

Exponential numbers, logarithm and properties, exponential, logarithmic and hyperbolic functions, the inverse of these functions with their graphs, complex numbers, basic notations of sequences and series, limit of basic functions, continuity.

 

 Some algebraic instructions and contents of calculus with their terminology, some expression that are used in pure and applied mathematics with their terminology. Writing and reading in math and some grammar of mathematics

 The function theory and limit of the functions, continuity of functions, derivative of the basic functions, derivative of trigonometric and inverse trigonometric functions, the mean value theorem of differentiation and its applications.

 Binary operations and fields, Matrices and Algebraic operations on matrices and inverse of matrices, System of linear equations, Gaussian elimination methods, Determinant and properties.

 Experimental and informal geometry, properties of plane and space figures, geometric constructions, the concept of angle, triangle, the elements of a triangle, application of triangles. Similarity theorems about triangles, application of similarity, trapezoid, parallelogram, equilateral quadrangle, rectangle, square, deltoid..

Vectors. Motion in one dimension. Motion in two dimensions. The laws of motion. Circular motion and other application of Newton’s laws. Work and energy. Potential energy and conservation of energy. Linear momentum and collisions. Rotation of a rigid body about a fixed axis. Rolling motion. Angular momentum and torque

Riemann integral, Definite and indefinite integral, area and volume of a solid of revolution, Vector calculus, functions of several variables, directional derivatives, gradient, vector-valued functions, sequences and infinite series, convergence and divergence, alternating series Power series, Taylor series.

Cramer’s rule, Vectors in R^2 and R^3, vector spaces , linear dependence and independence, basis and dimension, Eigen values and eigenvectors, Matrix representation of linear transformations, inner product space, diagonalization of matrix, orthogonal projections and Gram-Schmidt orthogonalization methods, Normal, Orthogonal and unitary operators, Linear functional and dual spaces

Theory of sets; mathematical logic; quantifiers; methods of proof in mathematics, Mathematical Induction, Relations and functions, Number systems; Natural, Integer, Rational, Reel and Complex number.

MATLAB is a numerical computing environment and programming language. Created by The Math Works, MATLAB allows easy matrix manipulation, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs in other languages. Although it specializes in numerical computing, an optional toolbox interfaces with the Maple symbolic engine, allowing it to be part of a full computer algebra system.

Electric fields. Gauss law. Electric potential. Capacitance and dielectrics. Current and resistance. Direct current circuits. Magnetic fields. Sources of the magnetic field. Faradays law. Inductance. Alternating current circuits.

Teacher trainees the basic concepts related to education, education, psychological, social, philosophical, economic, historical, legal basis, structure and problems of the Turkish educational system, radical views on education and introductory information to gain a new understanding.

Mathematical language, writing in math, reading in math, speaking in math, grammar in math, mathematical English, academic writing skills in math, academic English in math, phrases and sentences only in math.

Binary operations, Introduction to group theory, Group of integer (mod n), symmetric group, subgroups, Lagrange’s theorem, factor groups, permutation groups, group homeomorphisms, isomorphism theorems.

This course involves “what is a complex number, binary operations on it, complex functions as mapping, Limit and Continuity of complex functions, Differentiation of Complex Functions, Cauchy- Reimann Equation and Some Elementary Functions”.

First-order differential equations, second-order linear equations, Wronskian, change of parameters, homogeneous and non-homogeneous equations, series solutions, Laplace transform, systems of first-order linear equations, boundary value problems, Fourier series.

Discrete probability theory with statistical applications. Counting techniques; random variables; distributions; expectations; hypothesis testing and estimation, with emphasis on discrete models.

Basic concepts in sets, accountability, boundedness, supremum/infimum, limits of sequence of numbers and functions, Cauchy condition, continuity.

Basic concepts, The importance and place of materials and tools in instructions, Choosing instructions materials and tools, design of visual materials, instructions materials and its effective usage, the examinations of students material development skills.

introduction to ring theory, ideals, ring homeomorphisms, divisibility, polynomial rings, Modules, Projective and injective modules, fields, field extensions, algebraic extensions, field of rational functions, Integral domains and field,  Kronecker’s theorem, finite fields.

Complex differentiation, Cauchy-Riemann equations, holomorphic functions, conformal mappings, contour integration, Cauchy’s theorem, Infinite Series, Taylor and Laurent series, open mapping theorem, maximum modulus principle, applications of the residue theorem.

General, particular and singular solution of the Des, existence and uniqueness theorems, general solutions of nth order linear Des, Initial value problems and Boundary value problems, Cauchy-Euler, Legendre Des, Laplace transformations and inverse Laplace transformations.

probability axioms, conditional probability; Bayes’ theorem; discrete random variables, moments, bounding probabilities, probability generating functions, standard discrete distributions; continuous random variables, uniform, normal, Cauchy, exponential, gamma and chi-square distributions, transformations, the Poisson process; bivariate distributions, marginal and conditional distributions, independence, covariance and correlation, linear combinations of two random variables, bivariate normal distribution; sequences of independent random variables, the weak law of large numbers, the central limit theorem; definition and properties of a Markov chain and probability transition matrices; methods for solving equilibrium equations, absorbing Markov chains..

Basic concepts, Scales using in Measurement, Validity of measurement tools, To measure learning of effective, Characteristics of multiple-choice test, Characteristics of other types of test, performance assessment, basic statistical concepts, Process of test development, item analysis

Differentiability, Riemann integrals, İntegration, sequences and series of  real numbers and functions, convergence of sequence and series and uniform convergence, metric spaces, Cauchy sequence, completeness.

Some significant inequalities, metric and normed spaces, Banach spaces, linear spaces; boundedness, convergence, null convergence, absolute convergence, linear operators, bounded linear operators, dual spaces, Basic principles of functional analysis, Hilbert spaces.

Fundamentals of logic, Sets, Relations, Functions, Sequences, General Cartesian Product and Cardinality, Metrics and Topologies, Continuous Functions, Function Spaces and Topological Groups.

Basic concepts for the field and the relationship between these concepts in field, legal basis for the field according to The Constitution and the Basic Law of National Education, The general objectives of the field teaching, the use of methods, techniques, equipment and materials. The analysis of Curriculum (goals, objectives, theme, unit, activity, etc.). The examination and evaluation of course, teacher and student workbooks

Classroom management, applying teaching in classroom, arrangement of classroom setting, sources of disordered behaviors, decreasing disordered behaviors and management of disordered behaviors, reward and punishment used for shaping behavior, teachers’ behaviors in classroom and managing problematic students.

Introduce the students the concept of scientific research, different principles, methods, and stages of scientific research; and to help them learn how to conduct a scientific research by giving them, besides the theoretical knowledge they are given in the classes, a small scale research project.

Consolidating the skills necessary for teaching Math at primary, secondary and High schools through observation and teaching practice in pre-determined secondary schools under staff supervision; critically analyzing the previously acquired teaching related knowledge and skills through further reading, research and in class activities in order to develop a professional view of the Mathematics Education field.

Basic concepts, guidance and counseling of students, the place of guidance and counseling in helping students, fundamentals and developments of guidance and counseling, kinds of guidance and counseling, the services in counseling, techniques of counseling, the organization and personnel in counseling, student recognition techniques, directory-teacher cooperation, the guidance assignment of the teacher

Normed spaces, completeness, functionals, Hahn-Banach theorem, duality, operators; Lebesgue measure, measurable functions, integrability, completeness of L-p spaces; Hilbert space; compact, Hilbert-Schmidt and trace class operators.

Gaining the mathematical skills defined at the new Mathematics Curriculum in the classroom, Reasons for the Fundamental Changes into the curriculum, Aims of Mathematics Teaching and Basic Principles of the Program, Vision, Approaches and Conceptual Structure of the Curriculum, Conceptual, Affective and Psychomotor Abilities in Mathematics Education Curriculum Problem Solving, Communication, Reasoning, Connection, Mathematical Thinking and Modeling, Constructivism: The role of the Teacher and Student Sample Video Watching for Classroom Instruction, Preparation for the Presentations .

The subjects of some observations and practices; examining a student in different ways like asking questions, instructions and explanations, administration of lecture and the control of class; evaluating the studies of student; planning the lecture, benefiting team the lecture books; group studies; class organization; preparing and using the studying sheets; the activities of micro teaching in class.

The development and the operations of arithmetic dating from the 5000s B. C. , the studies made on mathematics in the subjects, Mathematics borning from daily needs, Ancient Egypt and Babel Mathematics, Old Greek mathematics; Thales, Pythagoras, Hippocrates and Eudoxous, Euclid, Archimedes and Eratosthenes, Apollonius Ptolemy, Heron and Diaphanous, Islamic world mathematicians; Harizmi and Banu Musa, Abu Kamil, Abul Vefa, Al-Karkhi, Omer Hayyam, el Biruni, Uluğ Bey, Kadızade, Ali Kuşçu, student presentations.

In this course, the student will develop a project based on one of the core areas (Algebra, Geometry, Analysis, or Probability and Statistics) appropriate for use in teaching.

This course presents the basic instructional principles and methods in education. It focuses on the principles of learning and teaching, the significance and necessity of being planned and organized in learning. To this end, this course will cover the basic principles of course design (e.g. yearly plans, lesson plans, and etc.) as well as basic methods and techniques in learning and teaching. In this course students will discover the ways to apply their relevant theoretical knowledge while learning how to utilize their teaching materials effectively. Students will also become conscious of teacher responsibilities and develop strategies to enhance quality in education.

This course is designed to provide information about how normal children develop and learn, as well as about the teaching process. Our knowledge about how children think, feel, and grow is far from complete, but what we do know can help teachers individualize teaching to meet children’s needs. Familiarity with the strengths and weaknesses of different classroom practices will enable student teachers to make better classroom choices. It will be studied that the scientific knowledge base of child development and educational psychology, and explore the implications for classroom practice.

This course is concerned with the educational needs of culturally and linguistically diverse students in Iraqian schools. The course will examine how cultural assumptions and biases affect teaching, and the role of multicultural education, anti-racism and cultural diversity policies at state and national levels. The needs of students from cultural backgrounds commonly encountered in mainstream classrooms such as Indigenous students, students from linguistically, culturally and religiously diverse backgrounds, students with special learning needs will be clarified, and teaching resources and inclusive strategies will be evaluated and developed.

Basic definitions, trees, Cayley’s formula, connectedness, Eulerian and Hamiltonian graphs, matchings, edge and vertex coloring, chromatic numbers, planar graphs, directed graphs, networks.

Computing is an essential part of modern mathematics. Many scientific endeavors require knowledge of sophisticated mathematical tools, which are computational in nature. This one-credit hour course is a hands-on introduction to computations as a problem solving tool in mathematics, using primarily the MATLAB platform. The labs will cover arrays and mathematical operations with arrays, representation of mathematical equations and functions using arrays, visualization of data and functions. MATLAB programming, including general program organization, m-files, built-in mathematical functions as well as user-defined functions, and symbolic math computations will be thoroughly discussed. Applications such as solving equations in one and several variables, finding min/max of a function, numerical integration will be highlighted. A more detailed list of topics is included in the course outline below.

Indexed family sets, Relations and Functions, finite and infinite sets, Cardinal numbers, The Schroder-Bernstein theorem, The Axiom al choice and some of its equivalent forms.

Probability theory, Bays theory, Multiple correlation, Multiple regression, T-test, -test (independence test), F-test, Quality control.

Solutions of nonlinear equations, Newton’s method, fixed points and functional iterations, LU factorization, pivoting, norms, analysis of errors, orthogonal factorization and least square problems, polynomial interpolation, spline interpolation, numerical differentiation, Richardson extrapolation, numerical integration, Gaussian quadratures, error analysis.

Review of the geometry of curves, Regular surfaces, First fundamental form, Orientation, Second fundamental form and the Gauss map, Vector fields, Minimal surfaces, Isometries, Gauss Theorem and equations of compatibility, Parallel transport, Geodesics and Gauss Bonet, The Exponential map, Some concepts from Global differential Geometry.

Factorization in Z, Diophantine equations, Congruence, Linear congruence, Fermat’s ,Euler’s and Wilson’s theorems, Euler’s function, The divisors of an integer, Perfect numbers, Quadratic congruencies, Pythagorean triplets, The case n=4 of Fermat’s Last theorem, sum of 2 and of 4 squares Pell’s theorem.

Basic definitions, syndrome decoding, BCH and cyclic codes, quadratic residue codes, weight distributions, relation to design theory.

First variation of a functional, necessary conditions for an extreme of a functional, Euler’s equation, fixed and moving endpoint problems, isoperimetric problems, problems with constraints, Legendre transformation, Noether’s theorem, Jacobi’s theorem, second variation of a functional, weak and strong extreme, sufficient conditions for an extreme, direct methods in calculus of variations, principle of least action, conservation laws, Hamilton-Jacobi equation

Concept, misconception, secondary school mathematics.

The mathematical elements of computer science including propositional logic, predicate logic, sets, functions and relations, combinatorics, mathematical induction, recursion, algorithms, matrices, graphs, trees, and Boolean logic, To recognize and express the mathematical ideas graphically, numerically, symbolically, and in writing.

Topology of real numbers; sequences, cluster points, continuity, theory of Differentiation and integration; elements of measure theory; infinite series.

Uniform continuity, Sequences and series of functions, Convergence and uniform convergence, Cauchy criterion, Weierstrass M-test, Dirichlet and Abel test, Infinite series, Arzelà-Ascoli theorem, Stone-Weierstrass theorem, Fourier series, inverse and implicit function theorems, Differentiation in , Chain rule and Mean value theorem.

This course allows students to understand the basic concepts of educational administration. Students will study and discuss Macau educational acts and decrees. They will also learn the basic theories related to educational administration, such as theories with regard to motivation, leadership, communication and organizational decision-making. Attempts will be made to make this course related to the educational reality in Macau.

This course presents the basic instructional principles and methods in education. It focuses on the principles of learning and teaching, the significance and necessity of being planned and organized in learning. To this end, this course will cover the basic principles of course design (e.g. yearly plans, lesson plans, and etc.) as well as basic methods and techniques in learning and teaching. In this course students will discover the ways to apply their relevant theoretical knowledge while learning how to utilize their teaching materials effectively. Students will also become conscious of teacher responsibilities and develop strategies to enhance quality in education.

A central focus of the course is policy analysis. We will be examining various bodies of evidence regarding the relationship beween education and different aspects of social development, but always with a view to what that evidence tells us about how one might alter educational policy (and practice) in particular places so as to contribute more effectively to social development.

Another core assumption of the course is that one cannot really understand the contemporary educational policy and practice issues and challenges we will be considering without some knowledge of their history. As I wrote in an essay we will be reading later in the course: “although I was not formally trained as an historian, I soon found that if I was to do my work well I had to become one. The contemporary educational problems with which I was dealing in various parts of the world simply could not be understood without a solid knowledge of their history.” This is true not only of developments within any particular nation/society, but of the comparative evidence and debates about it, which have been developing over many years. Thus the readings (and films) you will 2 encounter in this course range from very contemporary (“fresh off the press” or in “pre-publication form”) to very “old” (“classics” of various types). As you may note some of these “classics” still seem very “fresh” in this early stage of a new millennium. This range will hopefully help us to get a better sense of that history and its influence and importance to understanding the “present.”

This course satisfies the Junior Year Writing requirement. Students will develop skills in writing, oral presentation, and team work. The first unit will focus on professional development. Students will learn about career and graduate school opportunities, practice interview skills, and create a resume and cover letter and a graduate school statement of purpose. In the second unit students will engage with the challenge of writing and speaking about mathematics and statistics to different audiences. The third unit will focus on research in mathematics and statistics and will culminate in an expository group paper on a research topic.

This 3-credit course will have two components. The first will be a weekly hour-long seminar where students will be introduced to and discuss fundamentals of teaching secondary math – common core, curriculum, assessment, and resources. The second credit hour will be earned through supporting basic math. This will involve coming to all classes, working with small groups, leading a whole-class discussion, and teaching a mini-lesson.

Project-based learning (PBL) answers the question “What do we want to know”? This course will show you the step-by-step process for laying the groundwork for implementing PBL in your classroom. You will learn how to promote student engagement through the use of PBL and will get to see PBL in action. You will also have the opportunity to see how teachers have successfully reached beyond the classroom to add to the PBL experience.