• ML606 - Philosophy (3 credits)

Consolidate philosophical knowledge for research in the fields of social sciences and humanities; enhance the theoretical philosophical foundation of the Vietnamese revolutionary path, especially in the period of renewal. Improve and enhance philosophical knowledge in the Political Theory curriculum at the university level to meet the training requirements of social science and humanities disciplines at the postgraduate level.

•  TN627 - Functional analysis (3 credits)

This course provides learners with basic knowledge of calculus including 5 chapters. Chapter 1 introduces the concept of normed space with contents such as the definition of normed space, subspace, quotient space, product space, finite-dimensional space, and continuous linear operators. Chapter 2 presents the Lp spaces. Chapter 3 discusses the basic principles of calculus. Chapter 4 studies the Hilbert space with concepts such as inner product, orthogonality, basis of the space, projection onto a closed subspace. Chapter 5 presents the adjoint, self-adjoint, compact operators, and spectrum of continuous linear operators.

• SP615 - Advanced Linear Algebra (3 credits) 

The course covers fundamental topics in mathematics such as prime numbers, divisibility, and basic number theory theorems. In addition, students will be reintroduced to the concept of greatest common divisor and the Euclidean algorithm. The course will also cover topics in congruence theory, the Chinese remainder theorem, Hensel's lemma, and primitive roots. Furthermore, students will study in depth topics such as square numbers, the order of elements modulo p, arithmetic functions, and Diophantine equations. Additionally, the application of mathematics in teaching secondary school mathematics is also emphasized in this course.

• Education and international integration (SP689)

This course will provide learners with knowledge about Vietnam's education and international integration, which includes three main parts:

- Vietnam's education before the requirements of globalization and international integration

- The trend of development of Vietnam's education in the context of globalization and international integration

- The comprehensive reform strategy of Vietnam's education in the context of the 4th industrial revolution and international integration

- The above content will help learners understand the actual situation and the demand for international integration of Vietnam's education, thereby raising the awareness and responsibility of teachers in the current educational context. 

•  Graduation thesis (SPT000)

This is a course that synthesizes knowledge of educational science and mathematics education, both in theory and practice, to contribute to the overall evaluation of the output quality of the training program for the Mathematics Theory and Teaching Methodology major. This course helps students carry out a scientific research activity in mathematics education with a specific topic based on the issues raised and directed in the process of studying the courses in the training program under the guidance and support of scientific advisors.

• SPT602 - Evaluation in Mathematics Education (3 credits)

In this course, students can enhance their understanding of evaluation science in general and evaluation in mathematics education in particular. Students can apply this knowledge to design assessments to evaluate student learning outcomes, learn how to plan and manage evaluation work in high schools. In addition, students have skills to assess the quality of a math test using modern evaluation theories and tools. Moreover, students also have access to some applications of information technology in testing and evaluating student learning outcomes.

•  SPT003 - Theme: Developing Mathematical Abilities for High School Students (3 credits)

This course will equip learners with knowledge of the general and specialized mathematical competencies of high school students, as well as teaching methods to develop and evaluate these competencies. The course consists of three main parts:

The general and specialized mathematical competencies of high school students

Teaching methods to develop mathematical competencies

Ways to evaluate mathematical competencies

These topics will help learners acquire the necessary knowledge to effectively teach and develop mathematical competencies in high school students. Developing mathematical competencies is a very important task for math teachers in the high school math program since 2019. Therefore, this task requires teachers to have a solid understanding of modern teaching and evaluation methods to successfully fulfill their duties in the context of comprehensive innovation in teaching and learning today.

This course meets the output standards: 6.1, 6.2, 6.3 in the Master's Degree Program in Principles and Methods of Mathematics Education. 

•  SPT004 - Theme on Active Teaching Methods in Mathematics Education (2 credits)

 This course focuses on in-depth study of teaching techniques and positive teaching methods such as inquiry-based learning, problem-based learning, project-based learning, and collaborative learning. Students have the opportunity to explore various models of active learning in teaching concepts, theorems, and problem-solving in mathematics. As a result, students can apply and further develop various models of active teaching in teaching mathematics. 

• SPT005 - Theme on Teaching Algebra and Calculus (2 credits)

Through this course, students are introduced to an overview of the history of Algebra and Analysis. Based on historical records, students can draw pedagogical conclusions for each specific teaching topic. From here, students have a more comprehensive perspective on both the scientific and pedagogical aspects of the knowledge in the textbook program in high school. Moreover, students will learn how to exploit the knowledge in the textbook, develop teaching methods for specific topics such as equations, systems of equations, inequalities, functions, continuous functions, limits, derivatives, integrals, etc., in order to develop mathematical qualities and abilities for students.

• SPT006 - Theme on Teaching Probability and Statistics (2 credits)

This course will equip learners with knowledge of probability and statistics in high school, along with teaching methods for these topics. The course is divided into three main parts:

Probability and statistics knowledge in high school since 2019

Teaching probability and statistics in high school

Some situations for teaching probability and statistics

These topics will help learners acquire the necessary knowledge to effectively teach probability and statistics in high school.

In the high school math curriculum since 2019, probability and statistics are one of the three main areas of the program. Therefore, teaching probability and statistics under new conditions is one of the biggest tasks and challenges for high school math teachers.

This course meets the learning outcomes standards 6.1, 6.2, 6.3 in the Master's program in Principles and Methods of Teaching Mathematics. 

• PT008 - Theme: History of Mathematics Subfields. (2 credits)

Through this course, students are introduced to an overview of the history of mathematics. This subject delves deep into the history of each branch of mathematics. As a result, students will gain a deeper understanding of the origins and development of each branch of mathematics, and enhance their understanding of the scientific foundations of related branches of mathematics in secondary education. In addition, students will recognize the significance, challenges, and methods of integrating the history of mathematics into mathematics education.

• SPT626 - Advanced elementary Geometry (3 credits) 

Elementary geometry is one of the difficult and important fields of high school mathematics. Therefore, this subject is developed not only to help learners form the foundation of elementary geometry but also to provide in-depth specialized knowledge of this field, along with the specific research methods of the geometry subject. The main content of the course focuses on the properties of the main objects in elementary geometry, such as points, lines, triangles, quadrilaterals, circles, and the relationships between these objects. The content of the course includes specialized knowledge about elementary geometry that is not or little equipped at previous educational levels. With that knowledge foundation, it will create conditions for learners to teach and research elementary mathematics well, improving their level in the future.

• SPT627 - Advanced Elementary Algebra (3 credits) 

This course provides students with knowledge of 3 corresponding topics in 3 chapters:

Chapter 1 presents methods for solving equations and inequalities using the function method. We can use the properties of functions such as continuity, monotonicity, maximum value, minimum value to solve equations and inequalities.

Chapter 2 will introduce basic function equations and build a way to solve them.

Finally, chapter 3 will present advanced counting methods. We can use set theory, mapping, sequences and formal power series to solve combinatorial problems. 

• SPT628 - Advanced Number Theory (3 credits) 

 This course presents the fundamental concepts of number theory, such as prime numbers, divisibility, and the basic theorems of number theory. In addition, students will be reintroduced to the concept of greatest common divisor and the Euclidean algorithm. Topics on congruence theory, the Chinese Remainder Theorem, Hensel's Lemma, and primitive roots will also be covered. Furthermore, in this course, students will delve deeper into square numbers, the order of elements modulo p, as well as arithmetic functions and Diophantine equations. Moreover, the application of number theory in teaching secondary mathematics is of particular interest and focus. 

• SPT629 - Didactic Theory (2 credits) 

This course introduces the didactic theories of mathematics according to the French school. These theories provide opportunities for students to approach teaching and learning mathematics differently from the Theory and Practice of Teaching Mathematics course. In addition, students will be equipped with techniques for analyzing textbooks, analyzing problem types, designing teaching situations, analyzing teacher's teaching practices, and more. In summary, students will be exposed to some professional practices that will help them develop their expertise. 

• SPT630 - Graph Theory and its Applications (3 credits) 

This course equips students with fundamental knowledge and practical applications in the field of graph theory. Practical problems are addressed through algorithm design.

The course meets the learning outcomes 6.1.c, 6.2.b, 6.3 in the curriculum for the Mathematics Department's Theory and Methods of Teaching program with a research-oriented focus.

• SPT631 - Modern Teaching Theories in Mathematics Education (3 credits) 

This course belongs to the specialized knowledge block. The course includes content related to modern teaching theories in Mathematics Education such as Behaviorism, Constructivist Teaching Theory, Realistic Mathematics Education (RME), Information Processing Theory, and Experiential Learning Theory. These teaching theories provide graduate students with many different perspectives, principles, and models of teaching. They are very useful for high school math teachers in effectively teaching secondary mathematics. 

•  SPT634 - Teaching Mathematics with Dynamic mathematics Software (3 credits)

This course includes topics related to the use of the dynamic math software GeoGebra in teaching mathematics at the secondary school level. The course content includes studying the features and functions of the GeoGebra math software and designing situations that support teaching different topics in the secondary school math curriculum using this software. GeoGebra is a useful open-source math software that is free and has been selected by the Ministry of Education and Training for introduction in secondary schools. 

• SPT639 - Connecting Mathematics to Reality in Mathematics Education (3 credits)

This course equips learners with fundamental knowledge on connecting mathematics with reality, basic principles and perspectives of Realistic Mathematics Education (RME), perspectives on mathematical modeling, and the role of information technology in connecting mathematics with reality. Additionally, learners will practice designing teaching situations according to RME theory and mathematical modeling, with the support of information technology, to enhance the effectiveness of teaching and learning mathematics in schools. 

• SPT643 - Research Methods in Mathematics Education (3 credits)

 The course includes topics related to developing a research project, research methods, and common research types in the field of Mathematics Education. An important point is that students are able to propose a scientific research topic in Mathematics Education and complete a research proposal, carry out the process of data collection and processing using appropriate research methods. Students will learn how to present a thesis or a scientific research product in accordance with proper standards and ensure its reliability.