Algebra II
General data
Course ID:  360MS12ALG2a 
Erasmus code / ISCED: 
11.102

Course title:  Algebra II 
Name in Polish:  Algebra II 
Organizational unit:  Faculty of Mathematics 
Course groups:  
ECTS credit allocation (and other scores): 
5.00

Language:  English 
Type of course:  obligatory courses 
Requirements:  Algebra I 0600FS12ALG1 
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 
Classes in period "Academic year 2022/2023" (past)
Time span:  20221001  20230630 
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MO TU W TH FR 
Type of class:  (unknown)  
Coordinators:  Tomasz Czyżycki, Aneta Sliżewska  
Group instructors:  (unknown)  
Students list:  (inaccessible to you)  
Examination:  Examination 
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