Algebra

MATH-310

Media

MATH-310 Algebra

Algebra_2024_lecture13_review

16.12.2024, 17:42

Review, solutions of old exam questions.

Algebra-2024-lecture12

09.12.2024, 17:55

Irreducible polynomials, finite fields

Algebra-2024-lecture_11

02.12.2024, 17:47

CRT for Euclidean domains, solving congruences in polynomial rings, irreducible elements. 

Algebra-2024-lecture10

25.11.2024, 17:26

Chinese remainder theorem, Euler's totient function, Euclidean domains, Polynomials with coefficients in a field. 

Algebra MATH-310- 2024-lecture_9

18.11.2024, 17:35

Ideals in a ring, quotient rings, ring homomorphisms, characteristic of a ring. 

Algebra-MATH-310_2024_lecture8

11.11.2024, 17:51

Rings, definition and examples. Zero divisors, integral domains. Ideals in a commutative ring. 

Algebra-2024-lecture-7

04.11.2024, 20:20

Classification of finite abelian groups

Algebra-MATH310-2024-lecture6

28.10.2024, 17:34

Sign of a permutation in a symmetric group. The alternating group. Conjugacy classes in S_n. The orbit-stabilizer theorem. The class equation of a finite group. 

Algebra-MATH-310-2024-lecture 5

14.10.2024, 18:09

Symmetric group, cycle notation, conjugation

Algebra MATH-310 2024 lecture 4

07.10.2024, 17:30

Elliptic curve group; dihedral group. Normal subgroups and quotient group. 

Algebra MATH-310 2024 Lecture 3

30.09.2024, 17:37

Groups, group homomorphisms, presentation of a group in generators and relations. 

Algebra-MATH310-lecture2-2024

23.09.2024, 17:49

Alg-2024-lecture 1

09.09.2024, 17:55

Properties of natural and integer numbers. 

Alg2023-13

18.12.2023, 18:06

Review: solutions of the exam 2019. 

Alg2023-12

11.12.2023, 17:37

Quotient of a PID over a maximal ideal is a field. Irreducible polynomials with coefficients in a field. Finite fields: construction, examples, properties, classification. 

Alg2023-11

04.12.2023, 17:39

CRT for Euclidean domains. Solving of congruences in polynomial rings with coefficients in a field. Units, associates, irreducible elements. Maximal ideal in a PID is generated by an irreducible element.

Alg2023-10

27.11.2023, 17:46

Chinese remainder theorem for commutative rings and for integers. Polynomial rings, degree of a polynomial. Euclidean domains. A Eucliddean domain is a PID. 


Alg2023-9

20.11.2023, 17:39

Principal ideals. Principal ideal domains. Ring homomorphisms. Subrings. Characteristic of a ring. Direct product of rings. 

Alg2023-8

13.11.2023, 17:32

Rings. Examples of commutative rings. Zero divisors. Integral domains and fields. Rings Z/nZ. Ideal in a commutative ring. Sum, product and intersection of two ideals. Examples. 

Alg2023-7

06.11.2023, 17:37

Cauchy's theorem. Classification of simple finite abelian groups. Direct product of C_n and C_m. Properties of a direct product of groups. Classification of finite abelian groups. Elementary divisors and invariant factors. 

Alg2023-6

30.10.2023, 17:48

Symmetric group, the sign of a permutation, the alternating group. Conjugacy classes in a symmetric group. 

Alg2023-5

23.10.2023, 17:41

Symmetric group. The cycle notation. Product of elements in S_n. Conjugation of elements in S_n. Presentation of an element as a product of disjoint cycles. The symmetric group is generated by transpositions. 

Alg2023-4

16.10.2023, 17:48

Group homomorphisms. The kernel and the image of a group homomorphism. Normal subgroups. The dihedral group D_n and an example of a normal subgroup in D_n. Digression: the elliptic curve group and the Lenstra factorization algorithm. 

Alg2023-3

09.10.2023, 17:32

Proof of the RSA main concept. Groups given by generators and relations. Homomorphisms of groups. Isomorphism and automorphism. Example of homomorphisms between cyclic groups.

Alg2023-2

02.10.2023, 17:54

RSA cryptosystem. Groups, subgroups, left cosets. Theorem of Lagrange. Theorems of Euler and Fermat. 

Alg2023-1

25.09.2023, 19:17

Lecture 1: Integers. Well ordering principle and Induction principle. Euclidean division. Bezout's theorem. The Euler totient function. 

38, Lecture 13 - 2021

20.12.2021, 18:30

Solutions of the 2018 exam. 

37, Lecture 12 -2021

13.12.2021, 18:51

When is a polynomial irreducible. Eisenstein's criterion. Quotients of polynomial rings with coefficients in a field over an ideal generated by an irreducible polynomial. Properties of finite fields. The group of units of a finite field is cyclic. Existence and uniqueness of a finite field of order p^n, where p is a prime and n>1. 

36, Lecture 11 -2021

06.12.2021, 18:23

Properties of Euclidean domains. Greatest common divisor, least common multiple in a Euclidean domain. The Chinese remainder theorem for polynomial ring with coefficients in a field. Solving congruences in a polynomial ring. An ideal is maximal in a PID if and only if it is generated by an irreducible element. A quotient ring A/I of a Euclidean domain is a field if and only if the ideal I  is maximal.  Irreducible elements in a polynomial rings. 

35, Lecture 10-2021

29.11.2021, 18:39

Chinese remainder theorem for two factors. CRT for integers: two and multiple factors. Application to solutions of systems of congruences. Multiplicativity of the Euler's totient function. Polynomial rings. The degree of a polynomial. Invertible elements in polynomial rings. Euclidean domains, examples. Polynomial ring with coefficients in a field is a Euclidean domain. A Euclidean domain is a principal ideal domain. Associates in an integral domain. 

34, Lecture 9 -2021

22.11.2021, 17:39

Ideals and congruence relations. Principal ideals. Principal ideal domains. Theorem: Z is a principal ideal domain. Ring homomorphisms. Example: homomorphisms between Z/nZ and Z/mZ. Characteristic of a ring, examples. 

33, Lecture 8 -2021

15.11.2021, 17:17

Division rings. Fields. A division ring is a domain. Ideal in a commutative ring. Intersection, sum and product of two ideals. Examples: intersection, sum and product of two ideals in Z. 

32, Lecture 7 -2021

08.11.2021, 18:37

Classification theorem for finite abelian group. Elementary divisors and invariant factors. Examples. Rings: definition and first examples. Zero divisors. Domains and integral domains. The ring Z/nZ of integers modulo n. 

31, Lecture 6 -2021

01.11.2021, 18:25

Orbit-stabilizer theorem. Conjugacy classes and centralizers. The class equation of a finite group. Conjugacy classes in a symmetric group. Example: conjugacy classes in S_4. Simple groups. Simple abelian finite groups are cyclic groups of prime order. Direct product of groups. 

30, Lecture 5 -2021

25.10.2021, 19:34

Symmetric group. Cycle notation. Disjoint cycles commute and any element of S_n is a product of disjoint cycles, uniquely up to the order of factors. Multiplication and conjugation in S_n. The sign of a permutation. The alternating group A_n. 

29, Lecture 4 - 2021

18.10.2021, 19:39

Application of Lagrange's theorem in group theory and in arithmetic. The group of units in Z_n. Euler's theorem and Fermat's little theorem. Normal subgroup and quotient group. The image and kernel of a group homomorphism. 

28, Lecture 3 - 2021

11.10.2021, 18:35

Normal subgroup. Dihedral group, definition and presentation in generators and relations. Cosets relative to a given subgroup. Lagrange's theorem. 

27, Lecture 2 - 2021

04.10.2021, 19:15

Groups, definition and first properties. Cyclic group of order n. Homomorphisms of groups. Subgroup and normal subgroup. 

26, Lecture 1, 2021

27.09.2021, 19:24

Integers

24, Lecture 13

07.12.2020, 18:14

Solution of the practice exam in Algebra. 

22, Lecture 12

30.11.2020, 20:30

Irreducible polynomials with coefficients in a field. The Eisenstein criterion. Quotients of polynomial rings. Order of the quotient field. Properties of finite fields. The splitting field of the polynomial. The group of units of a finite field is cyclic. For any prime p and positive natural n there exists a unique finite field K of p^n elements. This field can be constructed as a quotient of F_p[x] over the ideal generated by an irreducible polynomial of degree n. 

20, Lecture 11

24.11.2020, 17:26

Properties of Euclidean domains. Chinese remainder theorem for the Euclidean domains. Corollary: Chinese remainder theorem for polynomial rings. Example. 

Maximal ideals. In a PID, maximal ideal is generated by an irreducible element. In a Euclidean domain, A/(a) is a field if and only if a is an irreducible element. Application to polynomial rings. Irreducible polynomials. 

18, Lecture 10

16.11.2020, 18:22

Chinese remainder theorem. The case of integers. Solving systems of congruences in integer numbers. The multiplicative property of the Euler totient function.

Polynomial rings. The degree of a polynomial over an integral domain. Euclidean division in polynomial rings. Definition of a Euclidean domain. Examples. A Euclidean domain is a PID. Units and associates in an integral domain. 

16, Lecture 9

09.11.2020, 15:32

Congruence relations in a ring. Relations between ideals in a commutative ring and congruence relations. Ring structure on the set of congruence classes in a ring. Principal ideals. Principal ideal domains (PID).  Z is a principal ideal domains. Ring homomorphisms. The kernel of a ring homomorphism is an ideal and the image a subring. Homomorphisms between Z/nZ and Z/mZ. Characteristic of a ring. Characteristic of a direct product of rings. 

14, Lecture 8

02.11.2020, 18:52

Division rings. Theorem: a division ring is a domain. The ring Z/nZ has no zero divisors if an only if n=p is a prime, in which case it is a field. Ideal in a ring. Intersection, sum and product of two ideals. Examples: ideals in Z. Ideals generated by a set. Theorem: A commutative ring A is a field if and only if the only ideals in A are {0} and A. 

12, Algebra, lecture 7

26.10.2020, 17:42

Theorem of classification of finite abelian groups. Elementary divisors and invariant factors.  

Rings: definitions and first properties. Zero divisors. Domains and integral domains. Z/nZ is an integral domain if and only if n is a prime. A ring A is a domain if and only if it satisfies the cancelation laws. 

10, Algebra, lecture 6

19.10.2020, 19:48

Action of a group on itself by conjugations. Conjugacy classes and centralizers. Class equation of a finite group. Direct product of groups, basic properties. Classification of finite abelian groups. 

8, Algebra, lecture 5

12.10.2020, 19:43

Symmetric group. Disjoint cycles. The cycle decomposition. Symmetric group is generated by transpositions. Even and odd permutations. The alternating group. Action of a finite group on a finite set. Orbit-stabilizer theorem. 

6, Algebra, lecture 4

05.10.2020, 23:51

Applications of Lagrange's theorem. Euler's theorem and Fermat's Little theorem. Classification of groups of order <=5. Quotient groups. Examples. The kernel of a group homomorphism is a normal subgroup. 

4, Algebra, lecture 3

29.09.2020, 14:25

Subgroups, normal subgroups. The dihedral group. Cosets in a group with respect to a subgroup. Lagrange's theorem. 

2, Algebra lecture 2

14.09.2020, 12:41

Euler's totient function. Definition of a group. Examples: group of flat rotations around the origin by multiples of 2pi/n, additive group of integers modulo n. Order of a group, order of an element. Homomorphisms and isomorphisms of groups.  Cyclic group of order n. Kernel of a homomorphism. 

1, Algebra, lecture 1

09.09.2020, 13:52

Organization of the course. 

Well-ordering and induction principles. Integer numbers, fundamental theorem of arithmetic. GCD, LCM. Euclidean algorithm to find the GCD of two integers. Bezout's theorem. 


Media

MATH-310 Algebra

Algebra_2024_lecture13_review

16.12.2024, 17:42

Review, solutions of old exam questions.

Algebra-2024-lecture12

09.12.2024, 17:55

Irreducible polynomials, finite fields

Algebra-2024-lecture_11

02.12.2024, 17:47

CRT for Euclidean domains, solving congruences in polynomial rings, irreducible elements. 

Algebra-2024-lecture10

25.11.2024, 17:26

Chinese remainder theorem, Euler's totient function, Euclidean domains, Polynomials with coefficients in a field. 

Algebra MATH-310- 2024-lecture_9

18.11.2024, 17:35

Ideals in a ring, quotient rings, ring homomorphisms, characteristic of a ring. 

Algebra-MATH-310_2024_lecture8

11.11.2024, 17:51

Rings, definition and examples. Zero divisors, integral domains. Ideals in a commutative ring. 

Algebra-2024-lecture-7

04.11.2024, 20:20

Classification of finite abelian groups

Algebra-MATH310-2024-lecture6

28.10.2024, 17:34

Sign of a permutation in a symmetric group. The alternating group. Conjugacy classes in S_n. The orbit-stabilizer theorem. The class equation of a finite group. 

Algebra-MATH-310-2024-lecture 5

14.10.2024, 18:09

Symmetric group, cycle notation, conjugation

Algebra MATH-310 2024 lecture 4

07.10.2024, 17:30

Elliptic curve group; dihedral group. Normal subgroups and quotient group. 

Algebra MATH-310 2024 Lecture 3

30.09.2024, 17:37

Groups, group homomorphisms, presentation of a group in generators and relations. 

Algebra-MATH310-lecture2-2024

23.09.2024, 17:49

Alg-2024-lecture 1

09.09.2024, 17:55

Properties of natural and integer numbers. 

Alg2023-13

18.12.2023, 18:06

Review: solutions of the exam 2019. 

Alg2023-12

11.12.2023, 17:37

Quotient of a PID over a maximal ideal is a field. Irreducible polynomials with coefficients in a field. Finite fields: construction, examples, properties, classification. 

Alg2023-11

04.12.2023, 17:39

CRT for Euclidean domains. Solving of congruences in polynomial rings with coefficients in a field. Units, associates, irreducible elements. Maximal ideal in a PID is generated by an irreducible element.

Alg2023-10

27.11.2023, 17:46

Chinese remainder theorem for commutative rings and for integers. Polynomial rings, degree of a polynomial. Euclidean domains. A Eucliddean domain is a PID. 


Alg2023-9

20.11.2023, 17:39

Principal ideals. Principal ideal domains. Ring homomorphisms. Subrings. Characteristic of a ring. Direct product of rings. 

Alg2023-8

13.11.2023, 17:32

Rings. Examples of commutative rings. Zero divisors. Integral domains and fields. Rings Z/nZ. Ideal in a commutative ring. Sum, product and intersection of two ideals. Examples. 

Alg2023-7

06.11.2023, 17:37

Cauchy's theorem. Classification of simple finite abelian groups. Direct product of C_n and C_m. Properties of a direct product of groups. Classification of finite abelian groups. Elementary divisors and invariant factors. 

Alg2023-6

30.10.2023, 17:48

Symmetric group, the sign of a permutation, the alternating group. Conjugacy classes in a symmetric group. 

Alg2023-5

23.10.2023, 17:41

Symmetric group. The cycle notation. Product of elements in S_n. Conjugation of elements in S_n. Presentation of an element as a product of disjoint cycles. The symmetric group is generated by transpositions. 

Alg2023-4

16.10.2023, 17:48

Group homomorphisms. The kernel and the image of a group homomorphism. Normal subgroups. The dihedral group D_n and an example of a normal subgroup in D_n. Digression: the elliptic curve group and the Lenstra factorization algorithm. 

Alg2023-3

09.10.2023, 17:32

Proof of the RSA main concept. Groups given by generators and relations. Homomorphisms of groups. Isomorphism and automorphism. Example of homomorphisms between cyclic groups.

Alg2023-2

02.10.2023, 17:54

RSA cryptosystem. Groups, subgroups, left cosets. Theorem of Lagrange. Theorems of Euler and Fermat. 

Alg2023-1

25.09.2023, 19:17

Lecture 1: Integers. Well ordering principle and Induction principle. Euclidean division. Bezout's theorem. The Euler totient function. 

38, Lecture 13 - 2021

20.12.2021, 18:30

Solutions of the 2018 exam. 

37, Lecture 12 -2021

13.12.2021, 18:51

When is a polynomial irreducible. Eisenstein's criterion. Quotients of polynomial rings with coefficients in a field over an ideal generated by an irreducible polynomial. Properties of finite fields. The group of units of a finite field is cyclic. Existence and uniqueness of a finite field of order p^n, where p is a prime and n>1. 

36, Lecture 11 -2021

06.12.2021, 18:23

Properties of Euclidean domains. Greatest common divisor, least common multiple in a Euclidean domain. The Chinese remainder theorem for polynomial ring with coefficients in a field. Solving congruences in a polynomial ring. An ideal is maximal in a PID if and only if it is generated by an irreducible element. A quotient ring A/I of a Euclidean domain is a field if and only if the ideal I  is maximal.  Irreducible elements in a polynomial rings. 

35, Lecture 10-2021

29.11.2021, 18:39

Chinese remainder theorem for two factors. CRT for integers: two and multiple factors. Application to solutions of systems of congruences. Multiplicativity of the Euler's totient function. Polynomial rings. The degree of a polynomial. Invertible elements in polynomial rings. Euclidean domains, examples. Polynomial ring with coefficients in a field is a Euclidean domain. A Euclidean domain is a principal ideal domain. Associates in an integral domain. 

34, Lecture 9 -2021

22.11.2021, 17:39

Ideals and congruence relations. Principal ideals. Principal ideal domains. Theorem: Z is a principal ideal domain. Ring homomorphisms. Example: homomorphisms between Z/nZ and Z/mZ. Characteristic of a ring, examples. 

33, Lecture 8 -2021

15.11.2021, 17:17

Division rings. Fields. A division ring is a domain. Ideal in a commutative ring. Intersection, sum and product of two ideals. Examples: intersection, sum and product of two ideals in Z. 

32, Lecture 7 -2021

08.11.2021, 18:37

Classification theorem for finite abelian group. Elementary divisors and invariant factors. Examples. Rings: definition and first examples. Zero divisors. Domains and integral domains. The ring Z/nZ of integers modulo n. 

31, Lecture 6 -2021

01.11.2021, 18:25

Orbit-stabilizer theorem. Conjugacy classes and centralizers. The class equation of a finite group. Conjugacy classes in a symmetric group. Example: conjugacy classes in S_4. Simple groups. Simple abelian finite groups are cyclic groups of prime order. Direct product of groups. 

30, Lecture 5 -2021

25.10.2021, 19:34

Symmetric group. Cycle notation. Disjoint cycles commute and any element of S_n is a product of disjoint cycles, uniquely up to the order of factors. Multiplication and conjugation in S_n. The sign of a permutation. The alternating group A_n. 

29, Lecture 4 - 2021

18.10.2021, 19:39

Application of Lagrange's theorem in group theory and in arithmetic. The group of units in Z_n. Euler's theorem and Fermat's little theorem. Normal subgroup and quotient group. The image and kernel of a group homomorphism. 

28, Lecture 3 - 2021

11.10.2021, 18:35

Normal subgroup. Dihedral group, definition and presentation in generators and relations. Cosets relative to a given subgroup. Lagrange's theorem. 

27, Lecture 2 - 2021

04.10.2021, 19:15

Groups, definition and first properties. Cyclic group of order n. Homomorphisms of groups. Subgroup and normal subgroup. 

26, Lecture 1, 2021

27.09.2021, 19:24

Integers

24, Lecture 13

07.12.2020, 18:14

Solution of the practice exam in Algebra. 

22, Lecture 12

30.11.2020, 20:30

Irreducible polynomials with coefficients in a field. The Eisenstein criterion. Quotients of polynomial rings. Order of the quotient field. Properties of finite fields. The splitting field of the polynomial. The group of units of a finite field is cyclic. For any prime p and positive natural n there exists a unique finite field K of p^n elements. This field can be constructed as a quotient of F_p[x] over the ideal generated by an irreducible polynomial of degree n. 

20, Lecture 11

24.11.2020, 17:26

Properties of Euclidean domains. Chinese remainder theorem for the Euclidean domains. Corollary: Chinese remainder theorem for polynomial rings. Example. 

Maximal ideals. In a PID, maximal ideal is generated by an irreducible element. In a Euclidean domain, A/(a) is a field if and only if a is an irreducible element. Application to polynomial rings. Irreducible polynomials. 

18, Lecture 10

16.11.2020, 18:22

Chinese remainder theorem. The case of integers. Solving systems of congruences in integer numbers. The multiplicative property of the Euler totient function.

Polynomial rings. The degree of a polynomial over an integral domain. Euclidean division in polynomial rings. Definition of a Euclidean domain. Examples. A Euclidean domain is a PID. Units and associates in an integral domain. 

16, Lecture 9

09.11.2020, 15:32

Congruence relations in a ring. Relations between ideals in a commutative ring and congruence relations. Ring structure on the set of congruence classes in a ring. Principal ideals. Principal ideal domains (PID).  Z is a principal ideal domains. Ring homomorphisms. The kernel of a ring homomorphism is an ideal and the image a subring. Homomorphisms between Z/nZ and Z/mZ. Characteristic of a ring. Characteristic of a direct product of rings. 

14, Lecture 8

02.11.2020, 18:52

Division rings. Theorem: a division ring is a domain. The ring Z/nZ has no zero divisors if an only if n=p is a prime, in which case it is a field. Ideal in a ring. Intersection, sum and product of two ideals. Examples: ideals in Z. Ideals generated by a set. Theorem: A commutative ring A is a field if and only if the only ideals in A are {0} and A. 

12, Algebra, lecture 7

26.10.2020, 17:42

Theorem of classification of finite abelian groups. Elementary divisors and invariant factors.  

Rings: definitions and first properties. Zero divisors. Domains and integral domains. Z/nZ is an integral domain if and only if n is a prime. A ring A is a domain if and only if it satisfies the cancelation laws. 

10, Algebra, lecture 6

19.10.2020, 19:48

Action of a group on itself by conjugations. Conjugacy classes and centralizers. Class equation of a finite group. Direct product of groups, basic properties. Classification of finite abelian groups. 

8, Algebra, lecture 5

12.10.2020, 19:43

Symmetric group. Disjoint cycles. The cycle decomposition. Symmetric group is generated by transpositions. Even and odd permutations. The alternating group. Action of a finite group on a finite set. Orbit-stabilizer theorem. 

6, Algebra, lecture 4

05.10.2020, 23:51

Applications of Lagrange's theorem. Euler's theorem and Fermat's Little theorem. Classification of groups of order <=5. Quotient groups. Examples. The kernel of a group homomorphism is a normal subgroup. 

4, Algebra, lecture 3

29.09.2020, 14:25

Subgroups, normal subgroups. The dihedral group. Cosets in a group with respect to a subgroup. Lagrange's theorem. 

2, Algebra lecture 2

14.09.2020, 12:41

Euler's totient function. Definition of a group. Examples: group of flat rotations around the origin by multiples of 2pi/n, additive group of integers modulo n. Order of a group, order of an element. Homomorphisms and isomorphisms of groups.  Cyclic group of order n. Kernel of a homomorphism. 

1, Algebra, lecture 1

09.09.2020, 13:52

Organization of the course. 

Well-ordering and induction principles. Integer numbers, fundamental theorem of arithmetic. GCD, LCM. Euclidean algorithm to find the GCD of two integers. Bezout's theorem. 


This file is part of the content downloaded from Algebra.
Course summary

General

Instructor: Anna Lachowska

Course organization: lectures and exercise sessions

Evaluation: Written exam and one graded written assignment

Algebra - Final exam : Monday, January 27, 15:15 - 18:15 


Lectures:   the first lecture on September 9

Mondays 15:15 - 17:00,  CM 1 1,  live streaming on Zoom.      

Lectures live streamed on Zoom and recorded. Zoom Passcode: 248350. 

Video recordings of lectures 2024 (and older): link 


Exercices:   Mondays 17:15 - 19:00,   CM 1 1.  


The first problem session will meet on Monday, September 9. 

Problem sets will appear on the Moodle webpage a few days before each session. 

Topics: 

  • Integers, well ordering, divisibility, Euclidean algorithm
  • Groups, subgroups, homomorphisms
  • Cosets, normal subgroups
  • Permutation groups, finite abelian groups 
  • Rings: zero divisors, integral domains
  • Ring homomorphisms, ideals
  • The Chinese remainder theorem
  • Polynomial rings over fields  
  • Finite fields, characteristic 

References:  

1. Polycopie Algebra MATH-310, A. Lachowska - J. Favre, available from the “print on demand” service

2. D.S. Dummit, R. M. Foote, Abstract Algebra. Wiley, Third Edition 

3. Page web:   http://moodle.epfl.ch     Math-310.

4. S. Lang, Undergraduate Algebra. Undergraduate texts in Mathematics. Springer-Verlag, Inc. New York, second edition, 1990. 

5.  L. Childs, A Concrete Introduction to Higher Algebra. Undergraduate texts in Mathematics, Springer-Verlag, Inc. New York, 1995.


Principal assistant: Vladyslav Shashkov

Assistants: 

Damien Bridel, Fabien Donnet-Monay, Mehdi Jelassi,  Kasimir de Guilhem de Lataillade. 




Resources

Course notes

Week 1

Week 2

Week 3

Week 4

Week 5

Week 6

Week 7

Week 8

Week 9

Week 10

Week 11

Week 12

Week 13

Assignments

Review materials

Organization of the final exam