**4.29 Analysis for One Variable Functions**

Analysis for One Variable Functions*Course:*

- Course code: SP111

- Credits: 3 credits.

- Hours: 45 theory hours and 90 self-study hours.

*Management unit:*

- Department: Mathematics Teacher Education.

- School: School of Education.

*Requisites:*

- Prerequisites: No.

- Corequisites: No.

*Course objectives:*

This course aims:

- To enable to apply specialized knowledge of analysis, ensure sufficient teaching capacity in high schools, to apply the modern analysis approach for clarifying the content of general analysis.

- To provide students with fundamental knowledge of analysis and meet the postgraduate study requirements.* *

- To develop students’ professional expertise.

- To enhance their use of standard Vietnamese in the major.

- To develop their ability to work independently or in a team, and to prepare self-study plans and to improve presentation skill; to study intently and responsibly and to be active in class participation.

*Brief description of the course:*

The course provides students in Mathematics Teacher Education with fundamental knowledge of the limit of a sequence, the limit of a function, the continuity of one variable functions, the derivative and differential of one variable functions, definite integrals, improper integrals, and the side-chain theory.

**4.30 Analysis for multivariable functions**

Analysis for multivariable functions*Course:*

- Course code: SP 112

- Credits: 3 credits

- Hours: 45 theory hours and 90 self-study hours.

*Management unit:*

- Department: Mathematics Teacher Education

- School: School of Education

*Requisites:*

- Prerequisites: SP 111

- Corequisites.

*Course objectives:*

This course aims:

- To provide students with fundamental knowledge of multivariable functions and differential equations.

- To meet the requirements of hard skills mentioned in the university undergraduate objectives.

- To meet the requirements of soft skills mentioned in the university undergraduate objectives.

- To meet the requirements of attitude mentioned in the university undergraduate objectives.

*Brief description of the course:*

The course provides students in Mathematics Teacher Education with fundamental knowledge of the limit of a sequence, the limit of a function, the continuity of multivariable functions, the derivative and differential of multivariable functions, the definite and improper integrals of multivariable functions.

**4.31 Complex analysis**

Complex analysis*Course:*

- Course code: SP115

- Credits: 02 credits

- Hours: 30 theory hours and 60 self-study hours.

*Management unit:*

- Department: Mathematics Teacher Education

- School: School of Education

*Requisites:*

**- **Corequisites: SP112

*Course objectives:*

This course aims:

- To provides students with solid knowledge of complex numbers and complex variable functions; understanding of the integral construction of complex variable functions, Cauchy’s integral theory, the side-chain theory of complex variable functions and surplus.

- To enable them to apply the knowledge learnt in doing exercises and solving problems in physics; to compare and evaluate the similarities between complex variable functions and real variable functions.

- To enable their self-study and self-improvement, their ability to update the knowledge using different sources; to organise and plan for group work and activities (group exercises); to present or report a topic in public.

- To develop their ability of analysis, synthesis and comparison; To form their critical thinking and lifelong learning skills; To work independently, creatively, and cooperatively; To collect and process information. To be able to communicate using academic language in a proficient and standardized way, and using IT tools and applications for teaching and learning activities as well.

- To enable them to recognise the importance of the course, the practical significance of the course and its application to practical problems; To promote students’ creativity, willingness and exploration in scientific research; To develop their intentness, discipline, sense of responsibility and patience in study and work, ethical manners of a scientist and a teacher.

*Brief description of the course:*

The course introduces the theory of functions of one complex variable. The course content refers to construction and representation of complex numbers, the Riemann sphere and the set of points on the complex plane. In addition, the course also presents the limit, continuity, derivative, and singularities of complex functions, some basic analytical functions of complex functions, and the relation between analytical functions and harmonic functions. The course also introduces some applications of elementary complex functions in solving elementary geometry, algebra, and trigonometry problems. Theoryal contents on the integral of complex functions like line integrals and Cauchy’s integral formula in simply and multiply connected domains; complex function series and surplus theory, and its application are presented very clearly and specifically in the learning process.

**4.32 Elementary geometry**

Elementary geometry*Course:*

- Course code: SG236

- Credits: 3 credits

- Hours: 45 theory hours and 90 self-study hours.

*Management unit:*

- Department: Mathematics Teacher Education

- School: School of Education

*Requisites:*

- Prerequisites: No

- Corequisites: No

*Course objectives:*

This course aims:

- To provide students with fundamental knowledge of direction angles, circles, spheres, polygons, polyhedral, geometric quantities (length, area, volume) and locus problems, geometric construction problems, and transformations.

- To form students’ mathematical and logical thinking to apply knowledge of elementary geometry into presenting elementary mathematics problems rigorously.

- To enable students to work in a team or independence, to make plans for self-study and develop presentation skills.

- To develop their intentness, responsibility and active contribution in study.

*Brief description of the course:*

The course provides students with definition of features in vector space, Affine space, Euclidean vector space, Euclidean space, and how to apply theory to solve problems from basic to advanced. They can understand the relations of the features in two and three dimensional spaces and general geometry. The course presents the method of studying geometry by algebraic tools and the construction of geometry from grouping viewpoint in particular, the general mathematical solutions such as inequalities, equations and inequation, system of equations, and geometry by coordinate method.

**4.33 General Topology**

General Topology*Course:*

- Course code: SP302

- Credits: 02 credits

- Hours: 30 theory hours and 60 self-study hours.

*Management unit:*

- Department: Mathematics Teacher Education

- School: School of Education

*Requisites:*

- Corequisites: SP101

*Course objectives:*

This course aims:

- To provide students with solid knowledge of topological spaces such as point types, open set, and closed set. To enable students to distinguish point types and compare topological spaces; to understand basic topological conditions; to distinguish axioms of countability; to prove properties of continuous, closed, and open mapping; to identify and compare types of Ti-spaces and prove Ti-spaces properties.

- To enable students to master fundamental knowledge and properties of metric spaces; to prove the convergence and completeness of metric spaces.

- To enable students to thoroughly understand, identify, and prove properties of spaces such as compact spaces, interconnected spaces, volume spaces, product spaces, and compact metric spaces.

- To enable their ability of self-study and self-improvement being able to update knowledge using different sources; to organise and plan for group work and activities (group exercises); to present or report a topic in public.

- To develop their ability of analysis, synthesis and comparison; to form their critical thinking and lifelong learning skills; to enable them to work independently, creatively, and cooperatively; to collect and process information.

- To enable them to communicate, use academic language in a proficient and standard way, and use IT tools and applications for teaching and learning activities; to promote creativity, inquiring mind and exploration in scientific research.

- To develop their attention, discipline, sense of responsibility and patience in study and work; to have work manners of a scientist and a teacher.

*Brief description of the course:*

The course introduces the fundamental knowledge of general topology such as topology on a set, open set, closed set, point types and other types of sets in topology. In addition, the concept of topological foundation and how to form a subspace are also presented in detail. The general topology also introduces axioms of countability, the relations between T- spaces. The concepts of continuous mapping, compact spaces, interconnected spaces, total-volume and product of topological spaces, and properties are also mentioned. The rest of the general topology is knowledge of metric space, convergence in the metric spaces, complete spaces; continuous mapping between metric spaces and compact metric spaces.

**4.34 Differential geometry**

Differential geometry*Course:*

- Course code: SP331

- Credits: 2 credits

- Hours: 30 theory hours and 60 self-study hours.

*Management unit:*

- Department: Mathematics Teacher Education

- School: School of Education

*Requisites:*

- Prerequisites: No.

- Corequisites: SP112; SP102.

*Course objectives:*

This course aims:

- To enable students to identify and interpret basic line and surface contents; to apply, calculate, and analyse characteristic quantities of curved lines and surfaces.

- To enable student to analyse and evaluate the geometric quantities of lines and surfaces, apply it to specific cases, thereby forming the skills of applying mathematics to the actual calculation.

- To create favourable conditions to improve students’ ability to research and cooperate in mathematics research.

- To enable students to recognise the differentiation and consistency of mathematics knowledge in many different fields; then they can expand their view of mathematics problems, forming a passion for further study and teaching.

*Brief description of the course:*

Geometry is an original and oldest field of mathematics. The studies of geometry have been laid the foundations since the period of BC, with the famous works of Euclid. Geometry has developed widely and diversely so far, in which there is a significant contribution of differential geometry to the strong and sustainable development of geometry. Differential geometry theory has many important practical applications. The aim of differential geometry is to study problems of geometry with the main tool-the differential calculus and derivation of functions (one or more variables). Therefore, it can be said that this is an important link of the two central areas of mathematics, geometry and mathematics analysis, and is the origin of geometric topology which is a rapidly developing field now.

**4.35 Measure theory and Lebesgue integration**

Measure theory and Lebesgue integration*Course:*

- Course code: SP318

- Credits: 02 credits

- Hours: 30 theory hours and 60 self-study hours.

*Management unit:*

- Department: Mathematics Teacher Education

- School: School of Education

No.*Requisites:**Course objectives:*

This course aims:

- To enable students to master knowledge and properties of measures and measurable functions; To apply the knowledge introduced to clarify and demonstrate the properties and characteristics of measures; to analyse, evaluate, and compare two convergence types: convergence in measure and almost sure convergence.

- To enable students to master the concept and basic properties of Lebesgue integration; to thoroughly understand the construction of the Lebesgue integrals and recognise the relation between Lebesgue integration and Riemann integrals; to calculate Lebesgue integration and construct integrals based on product measures.

- To enable students’ ability of self-study and self-improvement, to update new knowledge from different sources; to organise and plan for group work and activities (group exercises); to present or report a topic in public.

- To develop students’ ability of analysis, synthesis and comparison; critical thinking and lifelong learning skills;

- To enable them to work independently, creatively, and cooperatively; to collect and process information; to communicate, use academic language in a proficient and standard way, and use IT tools and applications for teaching and learning activities; to promote creativity, willingness and exploration in scientific research.

- To develop students’ intentness, discipline, sense of responsibility and patience in study and work; to form their ethical manners of a scientist and a teacher.

*Brief description of the course:*

The course introduces the theory of one complex variable function. The course content refers to complex number construction and representation, the Riemann sphere and the set of points on the complex plane. In addition, the course also presents the limit, continuity, derivative, and singularities of complex functions, some basic analytical functions of complex functions, and the relation between analytical functions and harmonic functions. The course also introduces some applications of elementary complex functions in solving elementary geometry, algebra, and trigonometry problems. Theoryal contents on the integral of complex functions like line integrals and Cauchy’s integral formula in simply and multiply connected domains; complex function series and surplus theory, and its application are also presented.

**4.36 Functional analysis**

Functional analysis*Course:*

- Course code: TN191

- Credits: 3 credits

- Hours: 45 theory hours and 90 self-study hours.

*Management unit:*

- Department: Department of Mathematics, Department of Mathematics Teacher Education.

- School: School of Natural Sciences, School of Education.

*Requisites:*

- Prerequisites: No.

- Corequisites: No.

*Course objectives:*

This course aims:

- To equip students with fundamental knowledge of functional analysis, normed spaces, Banach spaces, and Hilbert spaces for understand the problems of continuous linear operator.

- To help students generalise and improve their knowledge of mathematical analysis with the foundation of sound theory. To help students with problem-solving skills in mathematics.

- To develop students’ mathematics research skills. To develop students’ synthesis, analysis, evaluation, and presentation skills.

- To develop the intentness and discipline in study and have ethical manners of a teacher.

*Brief description of the course:*

The functional analysis course provides students with the knowledge of standard linear spaces, linear operators and conjugate spaces, the basic principles of functional analysis, and Hilbert space.

**4.37 Group theory**

Group theory*Course:*

- Course code: SP303

- Credits: 2 credits

- Hours: 30 theory hours and 60 self-study hours.

*Management unit:*

- Department: Mathematics Teacher Education

- School: School of Education

*Requisites:*

- Prerequisites: No

- Corequisites: SP101, SP102

*Course objectives:*

This course aims:

- To enable students to acquire knowledge of group structures such as groups, subgroups, standard subgroups, quotient groups, group homomorphism; some applications of cyclic groups in solving a number of arithmetic problems such as Fermat's theorem, Euler's theorem, and other applications in arithmetic; some finite group structures such as symmetric groups, Sylow p-subgroup, solvable groups; to apply the knowledge of this course to solving some problems in Galois theory and some other problems in algebraic structures such as ring, field, and modular structure.

- To enable students to analyse and synthesise learned knowledge to find out new knowledge by small exercises and class reports; to work effectively in team or independence through classroom activities and extra tasks.

- To promote students’ ability to work independently and cooperatively in an effective manner.

- To develop their intentness in scientific topics and have a desire to study more about different sources of knowledge related to this course.

*Brief description of the course:*

The course provides students with basic concepts of group structures such as groups, subgroups, standard subgroups, quotient groups and group homomorphism. It presents some applications of cyclic groups in solving some arithmetic problems such as Fermat's theorem, Euler's theorem, and other applications in arithmetic. Moreover, the course also introduces some finite group structures like symmetric groupsand Sylow p-subgroup, etc. In particular, it presents the concept of solvable groups to provide students with insights into this group structure and can apply to solve problems in Galois theory and other problems in algebraic structures.

**4.38 Ring and field theory**

Ring and field theory*Course:*

- Course code: SP085

- Credits: 3 credits

- Hours: 45 theory hours and 90 self-study hours.

*Management unit:*

- Department: Mathematics Teacher Education

- School: School of Education

*Requisites:*

- Prerequisites: No

- Corequisites: SP303

*Course objectives:*

This course aims:

- To provide students with the knowledge of ring structures such as rings, subrings, ideal, quotient rings, homomorphism rings; field and entire domain structures; ring structures of quotients, prime ideals and maxima; to enable them to apply knowledge of the course to the construction of main rings, ring of Gaussian integers, Euclidean rings, and polynomial rings.

- To enable students to analyse and synthesise knowledge learnt to find out new knowledge by small exercises and class reports; to work effectively in a team and independently through classroom activities and extra tasks.

- To promote students to work independently and cooperatively in an effective manner.

- To develop students’ interest in scientific topics and different sources of knowledge related to this subject matter.

*Brief description of the course:*

The course provides learners with basic concepts of ring structures such as rings, subrings, ideal, quotient rings, homomorphism rings, field, and entire domains. In addition, the course has several special rings such as ring of quotients, main rings, ring of Gaussian integers, Euclidean rings, and polynomial rings. The relations between these rings are given from that point. In addition, the course also provides a number of applications in solving arithmetic problems on prime domains as well as polynomial problems.

**4.39 Modules over commutative rings**

Modules over commutative rings*Course:*

- Course code: SP321

- Credits: 02 credits

- Hours: 30 theory hours and 60 self-study hours.

*Management unit:*

- Department: Mathematics Teacher Education.

- School: School of Education.

*Requisites:*

- Prerequisites: SP102.

- Corequisites: SP085.

*Course objectives:*

This course aims:

- To provide students with fundamental knowledge of constructing modular structures on commutative rings and constructing matching sequences on modules.

- To enable students to analyse, simplify, and diversify the concepts of modular structures; to apply the concept of matching sequences for forming features and relations between modules.

- To develop students’ teamwork and presentation skills.

- To enhance their awareness of the importance of constructing modular structures.

*Brief description of the course:*

The course provides students with fundamental knowledge of commutative algebra such as modules, module homomorphism, and matching sequences. It also provides students knowledge of how to build special modules such as free modules, Noether modules, Artin modules, localization of modules, and the tensor product of modules. In addition, the course content presents abstract concepts in a simplified way as well as diversifies examples to help students understand the essential meaning of modules.

**4.40 Number theory**

Number theory*Course:*

- Course code: SP103.

- Credits: 2 credits.

- Hours: 30 theory hours and 60 self-study hours.

*Management unit:*

- Department: Mathematics Teacher Education

- School: School of Education.

*Requisites:*

- Prerequisites: No

- Corequisites: No

*Course objectives:*

This course aims:

- To enable students to acquire knowledge of forming systems of numbers and equations, and system of congruence equations.

- To enable students to solve general arithmetic problems, build mathematical models, and solve practical problems.

- To develop students’ teamwork and presentation skills, a sense of responsibility, willingness to learn, and support to others.

*Brief description of the course:*

The course shows how to form sets of numbers, their calculations and features. The content is also about how natural numbers could be written in many different numeral systems such as decimal, binary, and hexadecimal systems. In the part of the ring of integers, divisible features are presented sufficiently such as concepts of divisibility and division with remainders, concepts of prime and composite numbers, equations and system of congruence equations. The course provides students with knowledge of how to represent real numbers in the form of continued fractions.

**4.41 Probability and Statistics - Mathematics Education**

Probability and Statistics - Mathematics Education*Course:*

- Course code: SP585

- Credits: 3 credits

- Hours: 45 theory hours and 90 self-study hours.

*Management unit:*

- Department: Mathematics Teacher Education

- School: School of Education

*Requisites:*

- Prerequisites: No

- Corequisites: SP111

*Course objectives:*

This course aims:

- To enable students to acquire fundamental knowledge of probability, random variables, discrete and continuous random variables. The statistics section provides students with knowledge of the problems: parameter estimation, statistical hypothesis testing, correlation, regression, etc.

- To develop students’ mathematics and logical thinking, to enable them to apply knowledge of probability to quantify the possibilities of uncertain phenomenon, recognise random phenomena in laws, and solve practical problems by statistical knowledge.

- To enable students to work in a team or independence, prepare plans for self-study and develop presentation skills.

- To develop students’ intentness, responsibility and active contribution in study

*Brief description of the course:*

The course provides students with the concept of probability and its formulas, random variables, the law of the probability distribution of random variables, and some special probability distribution laws. Also, it introduces basic and important problems of statistics such as the parameter estimation problem, the statistical hypothesis testing problem, correlation and regression.

**4.42 Linear Programming**

Linear Programming*Course:*

- Course code: SP304

- Credits: 2 credits

- Hours: 30 theory hours; 60 self-study hours.

*Management unit:*

- Department: Mathematics Teacher Education

- School: School of Education

*Requisites:*

- Prerequisites:

- Corequisite: SP102

*Course objectives:*

This course aims:

- To provide students with knowledge of linear programming; to enable them to solve well, completely the linear programming problem by using simplex algorithm, simplex algorithm extending problem M, simplex algorithm extending 2-phase problem; to understand well and apply duality theory to solve problems in practice; to apply the knowledge to solve transportation problems by using distribution algorithm, and solve special transportation related to practical applications; to set up mathematical modeling for practical problems and solve problems by using mathematical planning theory.

- To develop students’ ability to analyze, synthesize knowledge learnt to find new knowledge through small exerc0ises, reports in class

- To promote students’ ability to work individually and work as a team effectively.

- To develop students’ intentness to learn about scientific issues; to enhance their interest, a desire to learn more other knowledge related to this course.

*Brief description of the course:*

* *This course introduces the following issues*:* problems of linear programming are solved by using the simplex and extended simplex methods, the duality theory, the transportation problems and the distribution method. The applicability is focused in this course. Issues at higher level related to linear programming are briefly introduced in the study process and are open issues for students to do small studies.

**4.43 Elementary Algebra **

*Course***:**Elementary Algebra

- Course code: SP131

- Credits: 3 credits

- Hours: 45 theory hours and 90 self-study hours.

*Management unit:*

- Department: Mathematics Teacher Education

- School: School of Education.

No.*Prerequisites:**Course objectives:*

This course aims:

- To enable students to master knowledge of elementary algebra in high school Mathematics programme, and apply the knowledge of elementary algebra in teaching Mathematics at high school.

- To enable students to analyze and synthesize documents in elementary algebra; to analyze and synthesize documents about elementary algebra, to improve elementary mathematics level, to apply knowledge at university to the mathematics teaching.

- To develop their interest in profession and perform a scientific manner.

*Brief description of the course:*

The course presents the contents of elementary algebra related to general mathematics including: functions, derivatives and basis properties; radical equations and inequalities; exponential, logarithmic equations and inequalities; solving trigonometric equations; inequalities and applications; applying the knowledge of elementary algebra to the teaching Mathematics.

**4.44 Affine and Euclidean Geometry**

Affine and Euclidean Geometry*Course:*

- Course code: SP084

- Credits: 3 credits

- Hours: 45 theory hours; 90 self-study hours.

*Management unit:*

- Department: Mathematics Teacher Education

- School: School of Education

*Requisites:*

- Prerequisites: SP102

- Corequisite: No.

*Course objectives:*

This course aims:

- To equip students with fundamental knowledge about the vector space, the Affine space, the Euclidean vector space, and the Euclidean space of dimension *n.*

- To guide students to systematize improve their knowledge of geometry mathematics.

- To train students’ mathematical and logical thinking, problem solving skills about the Affine space, Euclidean vector space, and Euclidean space to present closely related mathematical problems.

- To enable them to acquire skills of teamwork, individual work, self-study planning, and presentation.

-To develop students’ intentness, sense of responsibility in study, and active contribution to the lessons.

*Brief description of the course:*

The course provides students with the concepts of properties in the Vector, Affine, Euclidean vector, and Euclidean spaces. It helps students know how to apply theories to solve from basic to advanced problems; moreover, students can see the relationships of the properties in two and three dimensions and high school geometry. Besides, it introduces to students the method of studying geometry by using algebraic tools, especially the construction of geometry from the group point of view. In particular, students also can study the high school mathematical solutions such as inequalities, equations, inequations, system of equations, and geometry by using coordinate method.

**4.45 Projective Geometry**

Projective Geometry*Course:*

- Course code: SP314

- Credits: 2 credits

- Hours: 30 theory hours; 60 self-study hours.

*Management unit:*

- Department: Mathematics Teacher Education

- School: School of Education

*Requisites:*

- Prerequisites: SP084

- Corequisite: No.

*Course objectives:*

This course aims:

- To equip students with fundamental knowledge of the projective space of dimension n, models and special properties in the n-dimensional space.

- To train students’ mathematical and logical thinking, and to eable them to apply knowledge of projective space to present closely related mathematical problems.

- To enable students to acquire skills of teamwork, individual work, self-study planning, and presentation.

- To develop students’ intentness, sense of responsibility in study, and active contribution to the lessons.

*Brief description of the course:*

The course provides students with issues of a projective space of dimension n and know how to apply theory to solve issues from basic to advanced. Students are required to understand the relationship between the Affine space and the projective space; relationship between projective geometry and Affine geometry to solve the Affine problem by projective means and vice versa. In addition, it also mentions specific issues in the real 2, 3-dimensional projective space in order to help students grasp things that are novel, easy to imagine and beneficial for teaching at high school in the future.

**4.46 Graph theory and Combinatorics**

Graph theory and Combinatorics*Course:*

- Course code: SG426

- Credits: 3 credits

- Hours: 45 theory hours and 90 self-study hours.

*Management unit:*

- Department: Mathematics Teacher Education

- School: School of Education.

*Requisites:*

- Prerequisites: No.

- Corequisite: No.

*Course objectives:*

This course aims:

- To provide students with knowledge of graph and combinatorial theory.

- To develop students’ skills of solving problems related to graph and combinatorics theory.

- To develop students’ skills of teamwork and presentation.

- To develop students’ intentness, spirit of learning and helping each other.

*Brief description of the course:*

Discrete mathematics has wide applications in practice in several different fields: mathematics, informatics, chemistry, biology, physics, and electronics. This course provides students with opportunities to research deeply and fully on issues related to graph and combinatorial theory. These ones are Euler cycle and path, Hamiltonian cycle and path, shortest path problem, plane graph, graph coloring problem, knowledge of fundamental and advanced counting principles. The applicability is focused in this course.

**4.47. History of Mathematics**

History of Mathematics*Course:*

- Course code: SP130

- Credits: 02 credits

- Hours: 30 theory hours and 60 self-study hours.

*Management unit:*

- Department: Mathematics Teacher Education

- School: School of Education

*Requisites:*

- Prerequisites: No.

- Corequisite: No.

*Course objectives:*

This course aims:

- To provide students with knowledge of the arising and development stages of Mathematics.

- To enable students to analyze and synthesize documents about the history of Mathematics in order to use in the teaching process at high schools.

- To develop students’ skills of teamwork and presentation.

- To enable students to use historical mathematics materials to improve the effectiveness of teaching Mathematics.

*Brief description of the course:*

The course introduces the development history of Mathematics and content related to general Mathematics. Its content presents the arising stages of Mathematics; the two outstanding Mathematics backgrounds of this period are Egyptian and Babylonian; Ancient Greek, Chinese, Indian and Arabic Mathematics backgrounds and typical mathematicians; to analyze the origin of Logarithms, Analytical and Classical Geometry and biographies of mathematicians with great contributions; to analyze the significance of three big events of modern mathematics: the basis of analytic mathematics; Non-Euclidean Geometry, Algebraic Structure.

**4.48 Numerical Analysis**

Numerical Analysis*Course:*

- Course code: SP082

- Credits: 02 credits

- Hours: 30 theory hours and 60 self-study hours.

*Management unit:*

- Department: Mathematics Teacher Education

- School: School of Education

*Requisites:*

- Corequisite: SP102, SP112

*Course objectives:*

This course aims:

- To enable students to master the basic concepts of error, and understand clearly the difference between computational mathematics and theory; to master the theory of interpolation, the approximation of functions by interpolation polynomials; to apply numerical methods to solve approximate some equations, system of algebraic equations and differential equations, approximate derivatives and integrations.

- To provide students with clear understanding of the approximation formulas, enable them to master the algorithm, to evaluate and compare the advantages and disadvantages of each method, to applying the learned approximation methods to specific problems, build an algorithm and evaluate the error of the calculation.

- To train students’ critical thinking, their ability to organize and plan for group work and activities (group exercises), their ability to present a report in public, to analyse and compare, synthesis; to form critical thinking and lifelong learning skills; work individually, to be creative and collaborate, as well as collect and process information.

- To train their ability to communicate, use fluently and standardly academic language. To help students realize the importance of the course and its practical significance and its application to real problems.

- To train their mathematical thinking, to promote creativity, to be eager to learn and explore in scientific research; to develop their intentness and sense of responsibility and patience in study and work; to have working style of a scientist and a teacher.

*Brief description of the course:*

The course introduces some approximate methods, and how to solve the approximate of a given problem. Specifically, it introduces approximate numbers and some types of errors, especially how to calculate errors in the calculation process. Moreover, it also presents some problems about interpolation theory or how to solve approximately a given function in the form of a number table such as Lagrange interpolation, Newton interpolation. Besides, students are also provided with derivative and integral solutions; approximate solution of algebraic and transcendental equations by using simple repeating methods, chord method and tangent method. Not only that, the course also introduces ways for approximate solutions of the system of linear equations and some other applications such as finding eigenvalues and eigenvectors. Another important application of the course is the approximate solution of differential equations using the Runge Kutta method level 4 and the Adams method.

**4.49 Introduction to Financial Mathematics**

Introduction to Financial Mathematics*Course:*

- Course code: SP308

- Credits: 02 credits

- Hours: 30 theory hours and 30 self-study hours.

*Management unit:*

- Department: Mathematics Teacher Education

- School: School of Education

*Requisites:*

- Prerequisites: No.

- Corequisite: No.

*Course objectives:*

The course aims;

- To enable students to to explain concepts of deterministic and stochastic financial Mathematics.

- To apply knowledge of Financial Mathematics to solve issues in practice.

- To develop students’ teamwork and presentation skills. .

- To develop students’ sense of responsibility, and the motivation of learning and helping each other

*Brief description of the course:*

The course presents fundamental contents of financial mathematics such as simple interests, compound interests, bonds, shares, investments, risks, and relevant issues.

**4.50. Partial Differential Equation**

Partial different equation*Course:*

- Course code: SP317.

- Credits: 2 credits

- Hours: 30 theory hours; 60 self-study hours.

*Management unit:*

- Department: Mathematics Teacher Education

- School: School of Education.

*Requisites:*

- Prerequisites: SP112.

- Corequisite: No

*Course objectives:*

This course aims;

- To provide students with fundamental knowledge of

- To provide students with the partial derivative equation.

- To meet the requirements of hard skills mentioned in the undergraduate education section.

- To meet the requirements of soft skills mentioned in the undergraduate education section.

- To meet the requirements of attitude mentioned in the undergraduate education section.

*Brief description of the course:*

The course provides basic contents of Fourier Series and Laplace Transforms; Overview of the partial different equation; the partial different equation level 1; The linear partial derivative equation for homogeneous constant coefficient; the derivative equation.

**4.51 Descriptive geometry**

Descriptive Geometry*Course:*

- Course code: SP329

- Credits: 2 credits

- Hours: 30 theory hours; 60 self-study hours.

*Management unit:*

- Department: Mathematics Teacher Education

- School: School of Education

*Requisites:*

- Prerequisites: No.

- Corequisite: SG236

*Course objectives:*

This course aims:

- To enable students to understand and explain fundamental contents of descriptive geometry; to calculate and analyse specific quantities of projections; to classify, explain and evaluate quantities with vertical projection and projection of points and lines; to apply to the actual calculation.

- To provide students with opportunities to improve their ability to research and cooperate in mathematics research.

- To enable students to recognize the consistency between theoryal mathematics and applied mathematics; From that, they can build a way of looking at the problem of mathematics according to the real-life approach, building a passion for learning and teaching in the future.

*Brief description of the course:*

The course refers to the methods of drawing a factor in three-dimensional space on the plane through projection methods, including the quantity factor of the object being considered.

**4.52 Professional English for Mathematics Teacher Education**

Professional English for Mathematics Teacher Education*Course:*

- Course code: SG376.

- Credits: 2 credits

- Hours: 30 theory hours; 60 self-study hours

*Management unit:*

- Department: Mathematics Teacher Education

- School: School of Education

*Requisites:*

- Prerequisites: XH025.

- Corequisite: No.

*Course objectives:*

This course aims:

- To equip students with specialized terminology to read and understand Mathematics documents in English.

- To link to the specialized documents in English to apply in research.

- To enable them to understand specialized documents in English to research and teah Mathematics.

- To enhance students’ self-study and to improve their English for future research and teaching of Mathematics.

*Brief description of the course:*

The course provides students with fundamental knowledge of English Mathematical terms, creating opportunities for students to access Mathematics materials written in English, to read, understand and translate these materials for Mathematics research and teaching in universities and high schools. The course also trains students to translate English - Vietnamese and Vietnamese - English Mathematics documents used in universities and high schools. After completing the course, students will have motivation to improve English for Mathematics at higher levels to serve the research and teaching Mathematics in high schools.

**4.53 Activities in Teaching and Learning Mathematics**

Activities in Teaching and Learning Mathematics*Course:*

- Course code: SP312.

- Credits: 2 credits

- Hours: 30 theory hours and 60 self-study hours.

*Management unit:*

- Department: Mathematics Teacher Education

- School: School of Education.

*Requisites:*

- Prerequisites: No.

- Corequisite: No.

*Course objectives:*

This course aims:

- To enable students to interpret the basic elements of Vygotski's Theory of Operation; the importance of learning motivation; basic actions and basic models in teaching mathematics concepts and theorems.

- To develop students’ skills of analysing and designing Mathematics teaching and learning activities according to the basic model of Activity theory.

- To enable students to use IT tools and applications to design learning activities; to develop their critical thinking skills, to make their action plans to improve professional capacity.

- To arouse students’ interest in their profession and educational research; their responsibility, work cooperation, and so on.

*Brief description of the course:*

*"Activity theory"* by Vygotsky and Leontiev is currently applied to the analysis of activities in several different fields. In the education, "teaching" and "learning" are two main inherent activities of a teaching process. Such division helps to make the constituent elements of a teaching process more clearly. On the basis of Vygotsky's arguments, this course introduces the Activity theory, the concept of motivation, learning actions and basic models in teaching mathematics at high schools.

**4.54 Thesis **

*Course:*

- Course code: New code

- Credits: 10 credits

- Hours: 300 theory hours

**Management unit:**

- Department: Mathematics Teacher Education

- School: School of Education

*Requisites:*

- Prerequisites: Students are required to accumulate 105 credits

- Corequisites: No

*Course objectives:*

This course aims:

- To presents students the necessary of scientific research; to provide them with knowledge related to students’ research topics.

- To enable students to conduct a scientific research; to acquire skills of teaching topics students select.

- To promote students’ ability to work individually and work as a team effectively; to master knowledge of the major.

*Brief description of the course:*

The course provides Mathematics students with an opportunity to conduct research on a topic that they have acquired before. Students can choose either a theoretical or experimental one. The course enables students to improve their ability to work individually, the way of presenting academic texts, and to approach to new research results in their research interest.

**4.55 Final Project **

Final Project*Course:*

- Course code: New code

- Credits: 4 credits

- Hours: 120 practice hours

*Management unit:*

- Department: Mathematics Teacher Education

- School: School of Education

*Requisites:*

- Prerequisites: Students are required to complete at least 105 credits

- Corequisites:** **

*Course objectives:*

This course aims:

- To enable students to understand the necessity of science research and to acquire knowledge of their research topic, skills of doing scientific research, espically the research topic of their interers.

- To promote learners’ skills of working independently and to develop the efficiency in teamwork and their interest in sciencetific research.

*Brief description of the course:*

** ** The course Final Project gives Mathematics students opportunities to delve into a specialized topic which they have studied. They can practice research skills by working on a specific topic of their interest. The study activities of this course develop students’ skills of working independently, presentation skills and insights into new research results in their major.

**4.56 Convex Analysis**

*Course:*

- Course code: SG245

- Credits: 2 credits

- Hours: 30 theory hours, 60 self-study hours.

*Management unit:*

- Department: Mathematics Teacher Education

- School: School of Education

*Requisites:*

- Prerequisites: no

- Corequisites: no

*Course objectives:*

This course aims:

- To enable students to recognize and explain the basic concept of convex analysis such as convex sets, convex functions, separation theorems of convex sets, polyhedral cones, and polyhedral sets. Students, then, can use, calculate and analyze maxima and minima concepts of elementary functions for general convex functions and the concepts of the stopping points to critical points of polyhedral sets; general inequalities for convex functions.

- To enable students to classify, explain and evaluate the models of specific problems related to convex functions and convex functions’ maxima and minima with conditions. Students can comprehend key concepts of forming and researching the attributes of convex functions, convex sets and issues related to elementary concepts such as straight lines, straight segments, etc. They can develop skills of generalisation and specialisation.

- To enable students to acquire research skills, analysis, synthesis and evaluation in Mathematics throughout the whole research project.

- To improve students’ ability to work independently or in group through projects and seminars; to develop their cooperation.

- To develop the constructive concepts for the development of diversified theor ties in mathematics. Students can acknowledge, familiarize and deal with issues in multiple aspects and different perspectives.

- To provide students with an opportunity to know about the latest research in modern mathematics, and understand the research directions of different scientist groups.

- To inspire students’ interest in studying and researching mathematics.

*Brief description of the course:*

This course is for senior students of Mathematics Teacher Education, (full-time, regular). At present, Convex Analysis is one of strongly developed fields in both Vietnam and the world. This theory plays an important role in both mathematics and applied one. This course focuses on major issues such as convex structures, convex optimisation and multi-faceted optimisation. It provides students with up-to-date knowledge, which is fundamental for postgraduate programmes in mathematics. The course familiarizes students with modern mathematics and necessary skills for study and research at higher levels in the future.

**4.57 Homological algebra**

Homological algebra*Course:*

- Course code: SG246

- Credits: 2 credits

- Hours: 30 theory hours, 60 self-study hours.

*Management unit:*

- Department: Mathematics Teacher Education

- School: School of Education

*Requisites:*

- Prerequisites: no

- Corequisites: SP102

*Course objectives:*

This course aims:

- To provide students with knowledge of the modularity theory over commutative rings such as modules, submodules, module homomorphisms, free modules, projective modules, injective modules, etc.

- To provide students with knowledge of exact sequences, short exact sequences, half exact sequences, projective solutions, definition of the category, functors, functors of Tensor, Hom, Tor, Ext and their properties.

- To train students’ mathematics and logical mindsets, analytical skills, to enable them to use both prior and up-to-date knowledge in doing small assignments and reports in class.

- To train students’ skills of working independently and in group, planning a study schedule and giving a presentation.

- To develop students’ intentness and responsibility in studying and researching scientific matters, and to arouse their interest in other sources of knowledge related to this course.

*Brief description of the course:*

The course provides students with some basic concepts of building the modularity theory over commutative rings such as modules, submodules, module homomorphisms, free modules, projective modules and injective modules. It introduces ways to construct the functors of Tensor, Hom, Tor and Ext by projective solutions. These functors measure how a module over a communicative ring R deviates from vector spaces in linear algebra.

**4.58 Galois Theory**

Galois Theory*Course:*

- Course code: SP311

- Credits: 2 credits

- Hours: 30 theory hours, 60 self-study hours.

*Management unit:*

- Department: Mathematics Teacher Education

- School: School of Education

*Requisites:*

- Corequisites: SP085

*Course objectives:*

This course aims:

- To provide students with knowledge of building theory of field extension and Galois Theory.

- To develop students’ skills of analysing, simplifying and diversifying the concepts of the theory of field extension and Galois Theory; using the concept of Galois Theory to build up solvability and unsolvability of the n degree equations.

- To train students’ skills of group work and presentation.

- To enable students to recognize the importance of building the theory of field extension and Galois Theory.

*Brief description of the course:*

The course provides students with some basic concepts of building up the theory of field extension such as algebraic extensions, normal extensions, separable extensions, Galois extensions, cyclic extensions, etc. Consequently, it illustrates how to define the intermediate fields of Galois extensions, finite field. Besides, this course also presents the unsolvability of quintic equations or higher. Students can apply the knowledge to solve problems with rulers and compasses.

**4.59 Trends of teaching mathematics**

Trends of teaching mathematics*Course:*

- Course code: SG244

- Credits: 2 credits

- Hours: 20 theory hours, 20 practice hours and 60 self-study hours.

*Management unit:*

- Department: Mathematics Teacher Education.

- School: School of Education

*Requisites:*

- Prerequisites: no

- Corequisites: no

*Course objectives:*

This course aims:

- To enable students to understand concepts of the didactic theory of case studies; to figure out the features, strengths and weaknesses of discovery teaching; to understand the models of discovery teaching and teaching with similar inferences.

- To train students’ skills of applying the theory of case studies to teaching mathematics at high school; skills of organization and teaching to explore mathematics concepts on different models and to convey mathematics theorems with scientific theories.

- To train students’ skills of using IT tools and applications to design learning activities, develop a mindset of study, and a professional development plan.

- To arouse students’ interest in the career development, education research and teaching, the concepts and theorems, and enable them to practice self-discipline and cooperation etc.

*Brief description of the course:*

This course introduces the basic concepts of the French didactic theory of case studies such as the teaching system "knowledge - teacher - student", didactic cases, didactic variable, teaching contracts and barriers. Besides, it provides students with the features and the models of discovery teaching such as teaching concepts with inductive models, teaching to explore theorems with hypothesis testing, teaching in the relationship between generality and particularity and teaching with similar inferences. This is a powerful tool for researching and applying active teaching methods in teaching mathematics in high schools.

**4.60 Maple**

Maple*Course:*

- Course code: SP327

- Credits: 2 credits

- Hours: 15 theory hours, 30 practice hours and 60 self-study hours.

*Management unit:*

- Department: Mathematics Teacher Education

- School: School of Education

*Requisites:*

- Prerequisites: no

- Corequisites: SP321

*Course objectives:*

This course aims:

- To provide students with knowledge of Maple software and applying it in solving problems.

- To train students’ skills of analysing the commands in Maple software and applying these commands in solving problems.

- To develop students’ skills of group work and presentation.

- To enable students to recognize the importance of building the commands’ structure in Maple.

*Brief description of the course:*

The course provides some concepts of the commands in Maple software. It enbles students to use them to solve the problems of arithmetic, algebra, linear algebra, group theory, analysis of single-variable functions and multi-variable functions, graphing, etc. Besides, this course also illustrates how to programme on Maple software. Particularly, it provides students with ways to apply Maple software in teaching and research.

**4.61 Set-Valued Analysis**

Set-Valued Analysis*Course:*

- Course code: SP328

- Credits: 2 credits

- Hours: 30 theory hours, 60 self-study hours.

*Management unit:*

- Department: Mathematics Teacher Education

- School: School of Education

*Requisites:*

- Prerequisites: No

- Corequisites: No

*Course objectives:*

This course aims:

- To enable students to recognise and explain the basic concepts of multivalued analysis such as continuity, semi-continuity, derivatives and differentials; to use, calculate and analyse the way to extend the concepts from a single-valued function to a multi-valued function in analysis; to classify, explain and evaluate the models of specific problems related to multiple-valued functions and multiple-valued vector functions.

- To provide students with basic concepts of developing from a single-valued problem, namely typical problems such as functions, limits of single-valued functions, to the respective cases of multiple-valued functions. Then students can practice skills of generalisation and specialization, skills of research, synthesis and evaluation in Mathematics, research projects and presentation of mathematics results.

- To improve students’ ability to work independently or in group via assignments and seminars.

- To introduce the new concepts and the diversified development of mathematics theories. - To familiarize students with problems and solutions from different aspects and perspectives; the latest research in modern mathematics, and different research directions.

- To arouse students’ interest in sciencetific research and mathematics.

- To train students to work in group, to develop their cooperation and good conduct in research.

*Brief description of the course:*

This course is for senior students (full time, regular) of Mathematics Teacher Education. The theory of Set-Valued Analysis is one of topical problems of modern mathematics theories. It plays a crucial role in optimality theory, Nonsmooth Analysis, Convex Analysis, etc. This new field interests domestic and international mathematicians.

This course provides students with basic concepts of the Multi-valued Analysis theory such as the continuity of multi-valued mappings, equilibrium points and fixed points of multi-valued mappings, derivative of multi-valued mappings, etc. This background enables students to continue to study, research on several specialized knowledge blocks in postgraduate programmes in Analysis and Optimality theory.