Study programme 2020-2021Français
Algebra II
Programme component of Bachelor's in Mathematics à la Faculty of Science

Students are asked to consult the ECTS course descriptions for each learning activity (AA) to know what special Covid-19 assessment methods are possibly planned for the end of Q3

CodeTypeHead of UE Department’s
contact details
US-B2-SCMATH-002-MCompulsory UEVOLKOV MajaS843 - Géométrie algébrique
  • VOLKOV Maja

of instruction
of assessment
HT(*) HTPE(*) HTPS(*) HR(*) HD(*) CreditsWeighting Term
  • Français
Français302000055.002nd term

AA CodeTeaching Activity (AA) HT(*) HTPE(*) HTPS(*) HR(*) HD(*) Term Weighting
S-MATH-011Algebra II3020000Q2100.00%
Programme component

Objectives of Programme's Learning Outcomes

  • Understand "elementary" mathematics profoundly
    • Use vector spaces, linear applications and the techniques associated with them
    • Understand and use the naive set theory
    • Understand basic algebraic structures
    • Manipulate previously acquired knowledge that appears in a question
    • Give examples and counterexamples for definitions, properties, theorems, etc.
  • Understand and produce strict mathematical reasoning
    • Write clearly and concisely
    • Use mathematical vocabulary and formalism appropriately
    • Make sense of formal expressions
    • Rely on a picture to illustrate a concept, rationale, etc.
  • Solve new problems
    • Abstract and manipulate theories and use these to solve problems
    • Adapt an argument to a similar situation
    • Use knowledge from different fields to address issues

Learning Outcomes of UE

Basic algebra: groups, commutative rings, fields. 
This course aims to present the essential material in undergraduate basic algebra. 

Content of UE

Groups: generated subgroups, factorisation of morphisms, canonical isomorphisms, centralisers, normalisers, dihedral groups, quaternion group, linear groups over finite fields. 
Commutative rings: prime ideals, maximal ideals, operations on ideals, Chinese remainder theorem, PID's and UFD's. 
Fields: field extensions, multiplicativity of degrees, algebraic and transcendental elements, roots of unity, minimal polynomials, extension degree computations. 

Prior Experience

"Algèbre I" course.

Type of Assessment for UE in Q2

  • Written examination

Q2 UE Assessment Comments

Not applicable

Type of Assessment for UE in Q3

  • Written examination

Q3 UE Assessment Comments

Not applicable

Type of Teaching Activity/Activities

AAType of Teaching Activity/Activities
  • Cours magistraux
  • Exercices dirigés

Mode of delivery

AAMode of delivery
  • Face to face

Required Reading


Required Learning Resources/Tools

AARequired Learning Resources/Tools
S-MATH-011Not applicable

Recommended Reading


Recommended Learning Resources/Tools

AARecommended Learning Resources/Tools
S-MATH-011M.A. Armstrong, Groups and Symmetry, Undergraduate Texts in Mathematics, Springer-Verlag.
D. Perrin, Cours d'Algèbre, Ellipses.
A. Chambert-Loir, Algèbre corporelle, Les Editions de l'Ecole polytechnique.

Other Recommended Reading

AAOther Recommended Reading
S-MATH-011Not applicable

Grade Deferrals of AAs from one year to the next

AAGrade Deferrals of AAs from one year to the next
(*) HT : Hours of theory - HTPE : Hours of in-class exercices - HTPS : hours of practical work - HD : HMiscellaneous time - HR : Hours of remedial classes. - Per. (Period), Y=Year, Q1=1st term et Q2=2nd term
Date de génération : 09/07/2021
20, place du Parc, B7000 Mons - Belgique
Tél: +32 (0)65 373111