Algebra II

General data

Course ID:	360-MS1-2ALG2a
Erasmus code / ISCED:	11.102 The subject classification code consists of three to five digits, where the first three represent the classification of the discipline according to the Discipline code list applicable to the Socrates/Erasmus program, the fourth (usually 0) - possible further specification of discipline information, the fifth - the degree of subject determined based on the year of study for which the subject is intended. / (0541) Mathematics The ISCED (International Standard Classification of Education) code has been designed by UNESCO.
Course title:	Algebra II
Name in Polish:	Algebra II
Organizational unit:	Faculty of Mathematics
Course groups:
ECTS credit allocation (and other scores):	(not available) Basic information on ECTS credits allocation principles: the annual hourly workload of the student’s work required to achieve the expected learning outcomes for a given stage is 1500-1800h, corresponding to 60 ECTS; the student’s weekly hourly workload is 45 h; 1 ECTS point corresponds to 25-30 hours of student work needed to achieve the assumed learning outcomes; weekly student workload necessary to achieve the assumed learning outcomes allows to obtain 1.5 ECTS; work required to pass the course, which has been assigned 3 ECTS, constitutes 10% of the semester student load. view allocation of credits
Language:	English
Type of course:	obligatory courses
Requirements:	Algebra I 0600-FS1-2ALG1 Algebra I 0600-MS1-2ALG1 Elementary Number Theory 0600-FS1-1ETL Elementary Number Theory 0600-MS1-1ETL Linear Algebra I 0600-FS1-1AL1 Linear Algebra I 0600-MS1-1AL1 Linear Algebra II 0600-FS1-1AL2 Linear Algebra II 0600-MS1-1AL2
Prerequisites (description):	(in Polish) The student has basic knowledge of Introduction to Mathematics, Elementary Number Theory and Linear Algebra and Algebra I.
Short description:	(in Polish) Course objectives: A student can apply the Sylow theorem to describe selected finite groups.A student efficiently uses permutation groups and the classification theorem for finitely generated abelian groups. A student understands the relationship between ideals and algebraic sets. A student understands and can use the Galois theory.
Full description:	(in Polish) Course profile: academic Form of study: stationary Course type: facultative Academic discipline: Mathematics, field of study in the arts and science: mathematics Year: 2, semester: 4 Prerequisities: Algebra I, Elementary Number Theory, Linear Algebra II lecture 30 h. exercise class 30 h. Verification methods: lectures, exercises, consultations, studying literature, home works, discussions in groups. ECTS credits: 5 Balance of student workload: attending lectures15x2h = 30h attending exercise classes 7x4h + 2h(preliminary teaching) = 30h preparation for classes 7x3h = 21h completing notes after exercises and lectures 7x2h = 14h consultations 5x2h = 10h preparation for control works 2x5h = 10h the final examination: preparation.and take 12h + 3h = 19h Quantitative description Direct interaction with the teacher: 74 h., 2 ECTS Practical exercises: 85 h., 3 ECTS
Bibliography:	(in Polish) 1. Paul M. Cohn " Basic Algebra: Groups, Rings and Fields", Springer Science & Business Media 2004. 2. Joseph J. Rotman "A First Course in Abstract Algebra: With Applications" Pearson Prentice Hall 2006. 3. Joseph Gallian "Contemporary Abstract Algebra" Cengage Learning 2016. 4. Gregory T. Lee "Abstract Algebra: An Introductory Course" Springer 2018. 5. I. N. Herstein "Abstract Algebra" Macmillan Pub 1990. 6. David S. Dummit, Richard M. Foote" Abstract Algebra" Wiley. 1999. 7. Thomas W. Hungerford "Algebra" Springer Science & Business Media, 2003.
Learning outcomes:	(in Polish) Student can formulate the most important theorems of general algebra, knows the basic theorem of algebra and understands its meaning KA6_WG03. Student knows examples of applications of general algebra methods in various branches of mathematics (for example, Fermat's little theorem in number theory) KA6_UW25. Student is able to use the most important theorems of general algebra to solve standard problems KA6_UW25. Student knows the basic structures and concepts of general algebra and can illustrate them with examples (permutation groups, polynomial rings, GF (p ^ n) fields) KA6_WG04. Student knows that the known algebraic structures exist and are important in various mathematical theories and can point out a specific example of the application of general algebra in reality (e.g. cryptography) KA6_WG02, KA6_WK01, KA6_WK03. Student notices analogies between the properties of various algebraic structures KA6_UW24.
Assessment methods and assessment criteria:	(in Polish) The overall form of credit for the course: final exam

This course is not currently offered.

Course descriptions are protected by copyright.
Copyright by University of Bialystok.