Bachelor's Degree in Mathematics: Training Educators in the Discipline
The IPA's Mathematics Department offers a three-year Bachelor's degree in Mathematics. This degree prepares future teachers and teaching specialists of mathematics for the Burundian and African context. The programme combines three inseparable pillars: mastery of mathematical content (algebra, geometry, analysis, statistics), a deep understanding of the cognitive processes of mathematical learning (problem solving, logical reasoning, conceptualisation), and the teaching skills to turn this expertise into effective and lasting learning for pupils.
This is not a programme in "abstract mathematics". It is practical preparation for helping generations of African learners build, understand and master mathematics. Students leave the Department not only as mathematics specialists, but as reflective educators able to adapt mathematics teaching to the specific context of Burundi.
The Department brings together an active intellectual community that debates, solves problems and experiments with teaching strategies together. Graduates work as secondary school teachers, teacher trainers and researchers in mathematics didactics in Burundi.
How the IPA trains mathematics teaching specialists: a progressive methodology
Three principles shape the Mathematics Department and reflect the IPA's teaching approach.
Principle 1: Cumulative progression from theory to teaching practice
The six semesters are not a series of isolated courses. They form a structured progression. The first two semesters lay the foundations: general mathematics, algebra, Euclidean geometry, an introduction to mathematical structures, and an introduction to learner psychology and cognitive development. In the third semester, students go deeper: linear algebra, analytical geometry, an introduction to calculus. In the fourth semester, the teaching focus becomes explicit: students take "Pedagogy and Didactics" — theory of teaching, setting learning objectives, teaching strategies, assessment of learning. In the fifth semester: "Special Didactics of Mathematics" — how to apply this theory specifically to mathematics teaching, dealing with learning errors, designing teaching sequences. In the sixth semester: teaching placements in real schools, supported by IPA supervisors.
This progression ensures that every student first masters the mathematical content in depth, then learns how to teach it, and then practises it in a real context.
Principle 2: Integrating contextualised and applied mathematics
The curriculum does not limit mathematics to abstract theory. Alongside the formal fundamentals, students explore applications of mathematics to the African context: statistics applied to development data, geometry in local architecture and engineering, mathematical modelling of natural phenomena. They discover how to teach mathematics not as an isolated discipline, but as a tool for understanding and solving real problems. This focus on usefulness makes teaching relevant and motivating for pupils.
Principle 3: Balancing theory and practice at every stage
Each course combines lectures (mathematical theory), tutorials (solving exercises and proofs), practical work (lesson design and teaching simulation), independent study (reflection on cognitive obstacles) and group work (collaborative learning). It is not "theory first, then practice". It is a constant alternation, so that every mathematical concept is immediately applied to a teaching situation and discussed in a group.
Structure of the Bachelor's in Mathematics: curriculum architecture
The Bachelor's degree in Mathematics is organised over three years (six semesters) according to the ECTS system. Each semester is worth 30 credits, i.e. 60 credits per year. The teaching load amounts to 450 hours per semester, i.e. 2,700 hours over the three years, divided between lectures (CM), tutorials (TD), practical work (TP), independent student work (TPE) and group work (TGE). At the end of the six semesters, students receive the official Bachelor's degree in Mathematics recognised by the University of Burundi.
Subject foundations
General mathematics, elementary algebra, Euclidean geometry, introduction to structures, child and adolescent psychology. Students gain systematic mastery of core mathematical content and a basic understanding of the learner's cognitive development.
Deeper knowledge and an introduction to pedagogy
Linear algebra, analytical geometry, differential and integral calculus, statistics and probability. In semester 4, an introduction to the principles of general pedagogy, setting learning objectives, teaching strategies, assessment of learning. Students recognise the distinction between subject mastery and teaching mastery.
Applied mathematics didactics
Students apply teaching principles to the specific context of mathematics teaching. Didactics of mathematical content, dealing with errors and conceptual obstacles, building teaching sequences, using tools (dynamic geometry, calculators, modelling).
Supervised practice in a professional setting
75 hours of teaching placements in a partner school. Students observe, teach, receive feedback from supervisors and write a report analysing their mathematics teaching practice.
| BAC I SEMESTER 1 | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| U.E | ECUE | Codes | Hours | Credits | |||||
| VHP60 | CM | TD | TP | TPE | TGE | ||||
| UE11: Fundamental Mathematics I | Algebra I | MAT1101 | 60 | 45 | 15 | 0 | 40 | 100 | 4 |
| Geometry I | MAT1102 | 60 | 45 | 15 | 0 | 40 | 100 | 4 | |
| UE12: Applied Mathematics I | General Physics I | MAT1103 | 60 | 45 | 0 | 15 | 40 | 100 | 4 |
| Descriptive Statistics | MAT1104 | 60 | 45 | 15 | 0 | 40 | 100 | 4 | |
| UE13: Fundamental Mathematics II | Analysis I | MAT1105 | 60 | 45 | 15 | 0 | 40 | 100 | 4 |
| Trigonometry | MAT1106 | 60 | 45 | 15 | 0 | 40 | 100 | 4 | |
| UE14: Support Courses I | French Expression Techniques | MAT1107 | 30 | 30 | 0 | 0 | 20 | 50 | 2 |
| Computing | MAT1108 | 30 | 15 | 0 | 15 | 20 | 50 | 2 | |
| History of Science | MAT1109 | 30 | 30 | 0 | 0 | 20 | 50 | 2 | |
| TOTAL | 450 | 300 | 750 | 30 | |||||
| BAC I SEMESTER 2 | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| U.E | ECUE | Codes | Hours | Credits | |||||
| VHP | CM | TD | TP | TPE | TGE | ||||
| UE25: Educational Psychology | Introduction to Psychology | MAT1210 | 30 | 15 | 15 | 0 | 20 | 50 | 2 |
| Child and Adolescent Psychology | MAT1211 | 30 | 15 | 15 | 0 | 20 | 50 | 2 | |
| Psychology of Learning | MAT1212 | 30 | 15 | 15 | 0 | 20 | 50 | 2 | |
| UE26: Fundamental Mathematics III | Analytical Mechanics I | MAT1213 | 60 | 45 | 0 | 15 | 40 | 100 | 4 |
| Algebra II | MAT1214 | 60 | 45 | 0 | 15 | 40 | 100 | 4 | |
| UE27: Support Courses II | Kiswahili | MAT1215 | 30 | 15 | 15 | 0 | 20 | 50 | 2 |
| TICE | MAT1216 | 30 | 15 | 15 | 0 | 20 | 50 | 2 | |
| Introduction to Information Retrieval | MAT1217 | 30 | 15 | 15 | 0 | 20 | 50 | 2 | |
| Technical English I | MAT1218 | 30 | 15 | 15 | 0 | 20 | 50 | 2 | |
| UE28: Fundamental Mathematics IV | Analysis II | MAT1219 | 60 | 45 | 15 | 0 | 40 | 100 | 4 |
| Geometry II | MAT1220 | 60 | 45 | 15 | 0 | 40 | 100 | 4 | |
| TOTAL | 450 | 300 | 750 | 30 | |||||
| ANNUAL Total | 900 | 600 | 1500 | 60 | |||||
| BAC II SEMESTER 3 | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| U.E | ECUE | Codes | Hours | Credits | |||||
| VHP | CM | TD | TP | TPE | TGE | ||||
| UE31: Fundamental Mathematics V | Algebra III | MAT2301 | 60 | 45 | 15 | 0 | 40 | 100 | 4 |
| Analysis III | MAT2302 | 60 | 45 | 15 | 0 | 40 | 100 | 4 | |
| UE32: Applied Mathematics II | General Physics II | MAT2303 | 60 | 45 | 15 | 0 | 40 | 100 | 4 |
| Analytical Mechanics II | MAT2304 | 60 | 45 | 15 | 0 | 40 | 100 | 4 | |
| UE33: Support Courses III | Introduction to Quantum Mechanics | MAT2305 | 60 | 45 | 15 | 0 | 40 | 100 | 4 |
| Descriptive Geometry | MAT2306 | 30 | 20 | 10 | 0 | 20 | 50 | 2 | |
| UE34: Fundamental Mathematics VI | Geometry III | MAT2307 | 60 | 45 | 15 | 0 | 40 | 100 | 4 |
| General Topology | MAT2308 | 60 | 45 | 15 | 0 | 40 | 100 | 4 | |
| TOTAL | 450 | 300 | 750 | 30 | |||||
| BAC II SEMESTER 4 | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| U.E | ECUE | Codes | Hours | Credits | |||||
| VHP | CM | TD | TP | TPE | TGE | ||||
| UE45: Fundamental Mathematics VII | Mathematical Logic | MAT2409 | 30 | 15 | 15 | 0 | 20 | 50 | 2 |
| Measure Theory | MAT2410 | 45 | 30 | 15 | 0 | 30 | 75 | 3 | |
| Functional Analysis | MAT2411 | 45 | 30 | 15 | 0 | 30 | 75 | 3 | |
| UE46: Applied Mathematics III | Probability and Analytical Statistics | MAT2412 | 60 | 45 | 15 | 0 | 40 | 100 | 4 |
| Operations Research | MAT2413 | 30 | 15 | 15 | 0 | 20 | 50 | 2 | |
| UE47: Support Courses IV | Citizenship Education | MAT2414 | 30 | 20 | 10 | 0 | 20 | 50 | 2 |
| Technical English II | MAT2415 | 30 | 20 | 10 | 0 | 20 | 50 | 2 | |
| Algorithms | MAT2416 | 60 | 45 | 15 | 0 | 40 | 100 | 4 | |
| UE48: Pedagogy and Didactics | General Pedagogy | MAT2417 | 30 | 20 | 10 | 0 | 20 | 50 | 2 |
| Setting Learning Objectives | MAT2418 | 30 | 20 | 10 | 0 | 20 | 50 | 2 | |
| Teaching and Learning Strategies | MAT2419 | 30 | 20 | 10 | 0 | 20 | 50 | 2 | |
| Assessment of Learning | MAT2420 | 30 | 20 | 10 | 0 | 20 | 50 | 2 | |
| TOTAL | 450 | 300 | 750 | 30 | |||||
| ANNUAL TOTAL | 900 | 600 | 1500 | 60 | |||||
| BAC III SEMESTER 5 | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| U.E | ECUE | Codes | Hours | Credits | |||||
| VHP | CM | TD | TP | TPE | TGE | ||||
| UE51: Fundamental Mathematics VIII | Complex Analysis | MAT3501 | 60 | 45 | 15 | 0 | 40 | 100 | 4 |
| Partial Differential Equations | MAT3502 | 45 | 30 | 15 | 0 | 30 | 75 | 3 | |
| UE52: Teacher Ethics | School Administration and Legislation | MAT3503 | 30 | 30 | 0 | 0 | 20 | 50 | 2 |
| Teacher Deontology | MAT3504 | 30 | 30 | 0 | 0 | 20 | 50 | 2 | |
| Mathematics Didactics | MAT3505 | 45 | 15 | 30 | 0 | 30 | 75 | 3 | |
| UE53: Applied Mathematics IV | Mathematical Astronomy | MAT3506 | 60 | 45 | 15 | 0 | 40 | 100 | 4 |
| Numerical Analysis and Programming | MAT3507 | 60 | 30 | 15 | 15 | 40 | 100 | 4 | |
| UE54: Related Courses | Mathematics Software | MAT3508 | 45 | 30 | 15 | 0 | 30 | 75 | 3 |
| Entrepreneurship | MAT3509 | 30 | 30 | 0 | 0 | 20 | 50 | 2 | |
| Time Series | MAT3510 | 30 | 30 | 0 | 0 | 20 | 50 | 2 | |
| TOTAL | 450 | 300 | 750 | 30 | |||||
| BAC III SEMESTER 6 | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| U.E | ECUE | Codes | Hours | Credits | |||||
| VHP | CM | TD | TP | TPE | TGE | ||||
| UE65: Fundamental Mathematics IX | Differential Geometry | MAT3611 | 45 | 30 | 15 | 0 | 30 | 75 | 3 |
| Projective Geometry | MAT3612 | 30 | 30 | 0 | 0 | 20 | 50 | 2 | |
| UE66: Applied Mathematics V | Computer-Based Statistical Computing | MAT3613 | 60 | 15 | 0 | 45 | 40 | 100 | 4 |
| Programming Languages | MAT3614 | 45 | 15 | 15 | 15 | 30 | 75 | 3 | |
| Dynamical Systems | MAT3615 | 45 | 30 | 15 | 0 | 30 | 75 | 3 | |
| UE67: Fundamental Mathematics X | Commutative Algebra | MAT3616 | 45 | 30 | 15 | 0 | 30 | 75 | 3 |
| Boolean Algebra | MAT3617 | 30 | 30 | 0 | 0 | 20 | 50 | 2 | |
| UE68: Teaching Practice | Didactics Exercises | MAT3618 | 45 | 0 | 15 | 30 | 30 | 75 | 3 |
| Teaching Placements | MAT3619 | 75 | 0 | 0 | 75 | 50 | 125 | 5 | |
| Placement Report | MAT3620 | 30 | 0 | 0 | 30 | 20 | 50 | 2 | |
| TOTAL | 450 | 300 | 750 | 30 | |||||
| ANNUAL TOTAL | 900 | 600 | 1500 | 60 | |||||
Where does studying mathematics lead? Careers and opportunities
Graduates of the Mathematics Department follow several career paths.
Secondary school teacher: Most become mathematics teachers in Burundian or regional secondary schools. With their IPA training, they are not ordinary teachers. They know didactics, can identify and address cognitive obstacles, and can train their colleagues.
Teacher trainer: Some graduates join in-service teacher training programmes, either at the IPA itself or at other institutions. Their teaching expertise makes them valuable in supporting other teachers and developing teaching resources.
Researcher in mathematics didactics: Students interested in research can go on to a Master's in Mathematics (Master's in Mathematics Didactics or Master's in Applied Mathematics), where they deepen their knowledge of pedagogy and the analysis of mathematical learning processes.
Educational coordinator or inspector: After several years of teaching experience, some graduates become school inspectors or educational coordinators at the ministry, where they help improve the quality of mathematics teaching nationwide.
Graduates report high job satisfaction: they teach, they make a difference to how learners understand mathematics, and their IPA training prepared them to do so effectively.
Admission requirements
To be admitted to the first year of the Bachelor's (BAC 1), applicants must meet the general admission conditions set by the University of Burundi:
- Hold the Burundian State Diploma (State Examination) or a qualification recognised as equivalent;
- Be placed in or admitted to an IPA department through the official admission procedure held each year;
- Submit an application file within the deadlines set by the Directorate of Academic Services.
For the procedure and the programme choice platform, see the Bachelor's Admissions page.