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Group Theory

Course Information

Course Name: Group Theory
Course Code: MAT5102
Programme: Bachelor of Education with Honours in Mathematics and Physics

Academic Year: 2024–2025
Course Lecturer:
Credits: 10
Level/Semester: Year III, Trimestre II
Delivery Mode: Face-to-face lectures, tutorials, mathematical proof sessions, assignments, and Moodle support.

Welcome Message

Welcome to Group Theory.

This course introduces the abstract algebraic structures known as groups and their applications in mathematics, physics, cryptography, and symmetry analysis.

Course Overview

The course covers binary operations, groups, subgroups, cyclic groups, permutation groups, cosets, normal subgroups, quotient groups, homomorphisms, isomorphisms, Lagrange's theorem, and applications of group theory.

Learning Objectives

Students should be able to:

Understand abstract algebraic structures.
Analyze finite and infinite groups.
Apply group operations.
Construct mathematical proofs.
Apply group theory in scientific fields.

Learning Outcomes

Students will be able to:

Explain concepts of group theory.
Analyze subgroup structures.
Apply homomorphisms and isomorphisms.
Solve abstract algebra problems.
Apply group theory to mathematics and physics.

Assessment Methods

Assignment: 10 Marks
Continuous Assessment Test (CAT): 10 Marks
Mid-Term Examination: 40 Marks
Final Examination: 40 Marks

Course Duration

15 Weeks

Teacher: Edison ISHIMWE

ATOMIC PHYSICS

The Atomic Physics course explores the structure, behavior, and interactions of atoms, focusing on the principles that govern atomic systems and their energy levels. Topics include the historical development of atomic models, quantum theory, electron configurations, atomic spectra, and fine structure. The course examines the interaction of atoms with electric and magnetic fields (Zeeman and Stark effects), spin-orbit coupling, and the principles of atomic transitions and radiation. It provides a foundation for understanding atomic-scale phenomena and their applications in spectroscopy, lasers, quantum optics, and modern technology. Emphasis is placed on both theoretical understanding and experimental techniques used in atomic physics.

Objectives

To understand the fundamental structure and properties of atoms based on quantum mechanics.

To trace the historical development of atomic models from classical to modern quantum theory.

To analyze atomic spectra and understand the origin of spectral lines.

To study the effects of external fields on atomic energy levels (e.g., Zeeman and Stark effects).

To introduce experimental techniques and applications related to atomic transitions and interactions.

Learning Outcomes:

Explain the structure of atoms using quantum mechanical principles.
Describe and compare atomic models such as Bohr’s model and the quantum mechanical model.
Interpret atomic spectra and calculate energy level transitions.
Analyze the effects of magnetic and electric fields on atomic systems (Zeeman and Stark effects).
Understand the concepts of spin, fine structure, and spin-orbit coupling.
Apply atomic physics concepts to technologies such as lasers, atomic clocks, and spectroscopy.
Solve problems involving electron configurations, selection rules, and transition probabilities.

Academic Year 2024-2025
Lecturer: Augustin SIWEGUSA

Teacher: content creator

Statistical Physics

Course Information

Course Name: Statistical Physics
Course Code: PHY5101
Programme: Bachelor of Education with Honours in Mathematics and Physics

Academic Year: 2024–2025
Course Lecturer:
Credits: 10
Level/Semester: Year III, Trimestre II
Delivery Mode: Face-to-face lectures, tutorials, problem-solving sessions, laboratory demonstrations, assignments, and Moodle support.