RES.18-012 | Spring 2022 | Undergraduate

Algebra II Student Notes

Lecture Notes

file
416 kB
mit18_702s22_lec_w_img.zip
pdf
301 kB
RES.18-012 (Spring 2022) Appendix: Dimensions of Irreducible Characters
pdf
2 MB
RES.18-012 (Spring 2022) Full Lecture Notes: Algebra II Student Notes
pdf
486 kB
RES.18-012 (Spring 2022) Lecture 1: Representations
pdf
492 kB
RES.18-012 (Spring 2022) Lecture 1: Representations
pdf
325 kB
RES.18-012 (Spring 2022) Lecture 10: Ideals in Polynomial Rings
pdf
325 kB
RES.18-012 (Spring 2022) Lecture 10: Ideals in Polynomial Rings
pdf
332 kB
RES.18-012 (Spring 2022) Lecture 11: More About Rings
pdf
332 kB
RES.18-012 (Spring 2022) Lecture 11: More About Rings
pdf
330 kB
RES.18-012 (Spring 2022) Lecture 12: Factorization in Rings
pdf
330 kB
RES.18-012 (Spring 2022) Lecture 12: Factorization in Rings
pdf
307 kB
RES.18-012 (Spring 2022) Lecture 13: More Factorization
pdf
307 kB
RES.18-012 (Spring 2022) Lecture 13: More Factorization
pdf
328 kB
RES.18-012 (Spring 2022) Lecture 14: Number Fields
pdf
328 kB
RES.18-012 (Spring 2022) Lecture 14: Number Fields
pdf
341 kB
RES.18-012 (Spring 2022) Lecture 15: Ideal Factorization
pdf
341 kB
RES.18-012 (Spring 2022) Lecture 15: Ideal Factorization
pdf
320 kB
RES.18-012 (Spring 2022) Lecture 16: Uniqueness of Ideal Factorization
pdf
320 kB
RES.18-012 (Spring 2022) Lecture 16: Uniqueness of Ideal Factorization
pdf
342 kB
RES.18-012 (Spring 2022) Lecture 17: Ideals in Quadratic Fields
pdf
342 kB
RES.18-012 (Spring 2022) Lecture 17: Ideals in Quadratic Fields
pdf
380 kB
RES.18-012 (Spring 2022) Lecture 18: The Ideal Class Group
pdf
380 kB
RES.18-012 (Spring 2022) Lecture 18: The Ideal Class Group
pdf
335 kB
RES.18-012 (Spring 2022) Lecture 19: Modules over a Ring
pdf
335 kB
RES.18-012 (Spring 2022) Lecture 19: Modules over a Ring
pdf
403 kB
RES.18-012 (Spring 2022) Lecture 2: Characters and the Direct Sum
pdf
403 kB
RES.18-012 (Spring 2022) Lecture 2: Characters and the Direct Sum
pdf
315 kB
RES.18-012 (Spring 2022) Lecture 20: Modules and Presentation Matrices
pdf
315 kB
RES.18-012 (Spring 2022) Lecture 20: Modules and Presentation Matrices
pdf
365 kB
RES.18-012 (Spring 2022) Lecture 21: Smith Normal Form
pdf
365 kB
RES.18-012 (Spring 2022) Lecture 21: Smith Normal Form
pdf
348 kB
RES.18-012 (Spring 2022) Lecture 22: Decomposition of Modules
pdf
348 kB
RES.18-012 (Spring 2022) Lecture 22: Decomposition of Modules
pdf
315 kB
RES.18-012 (Spring 2022) Lecture 23: Noetherian Rings
pdf
315 kB
RES.18-012 (Spring 2022) Lecture 23: Noetherian Rings
pdf
335 kB
RES.18-012 (Spring 2022) Lecture 24: Fields
pdf
335 kB
RES.18-012 (Spring 2022) Lecture 24: Fields
pdf
326 kB
RES.18-012 (Spring 2022) Lecture 25: Field Extensions
pdf
326 kB
RES.18-012 (Spring 2022) Lecture 25: Field Extensions
pdf
338 kB
RES.18-012 (Spring 2022) Lecture 26: Finite Fields
pdf
338 kB
RES.18-012 (Spring 2022) Lecture 26: Finite Fields
pdf
388 kB
RES.18-012 (Spring 2022) Lecture 27: Finite Fields (continued)
pdf
388 kB
RES.18-012 (Spring 2022) Lecture 27: Finite Fields (continued)
pdf
369 kB
RES.18-012 (Spring 2022) Lecture 28: Geometry of Function Fields
pdf
369 kB
RES.18-012 (Spring 2022) Lecture 28: Geometry of Function Fields
pdf
311 kB
RES.18-012 (Spring 2022) Lecture 29: Galois Theory
pdf
311 kB
RES.18-012 (Spring 2022) Lecture 29: Galois Theory
pdf
349 kB
RES.18-012 (Spring 2022) Lecture 3: Irreducible Representations
pdf
349 kB
RES.18-012 (Spring 2022) Lecture 3: Irreducible Representations
pdf
315 kB
RES.18-012 (Spring 2022) Lecture 30: Main Theorem of Galois Theory
pdf
315 kB
RES.18-012 (Spring 2022) Lecture 30: Main Theorem of Galois Theory
pdf
375 kB
RES.18-012 (Spring 2022) Lecture 31: Applications of the Galois Correspondence
pdf
375 kB
RES.18-012 (Spring 2022) Lecture 31: Applications of the Galois Correspondence
pdf
355 kB
RES.18-012 (Spring 2022) Lecture 32: Solving Polynomial Equations
pdf
355 kB
RES.18-012 (Spring 2022) Lecture 32: Solving Polynomial Equations
pdf
330 kB
RES.18-012 (Spring 2022) Lecture 33: Symmetric Polynomials and the Discriminant
pdf
330 kB
RES.18-012 (Spring 2022) Lecture 33: Symmetric Polynomials and the Discriminant
pdf
370 kB
RES.18-012 (Spring 2022) Lecture 34: Solving Polynomial Equations (continued)
pdf
370 kB
RES.18-012 (Spring 2022) Lecture 34: Solving Polynomial Equations (continued)
pdf
335 kB
RES.18-012 (Spring 2022) Lecture 35: Final Remarks
pdf
335 kB
RES.18-012 (Spring 2022) Lecture 35: Final Remarks
pdf
425 kB
RES.18-012 (Spring 2022) Lecture 4: The Main Theorem
pdf
425 kB
RES.18-012 (Spring 2022) Lecture 4: The Main Theorem
pdf
373 kB
RES.18-012 (Spring 2022) Lecture 5: Characters and Schur’s Lemma
pdf
373 kB
RES.18-012 (Spring 2022) Lecture 5: Characters and Schur’s Lemma
pdf
355 kB
RES.18-012 (Spring 2022) Lecture 6: Orthonormality of Characters
pdf
355 kB
RES.18-012 (Spring 2022) Lecture 6: Orthonormality of Characters
pdf
476 kB
RES.18-012 (Spring 2022) Lecture 7: Proof of the Main Theorem
pdf
476 kB
RES.18-012 (Spring 2022) Lecture 7: Proof of the Main Theorem
pdf
316 kB
RES.18-012 (Spring 2022) Lecture 8: Rings
pdf
316 kB
RES.18-012 (Spring 2022) Lecture 8: Rings
pdf
338 kB
RES.18-012 (Spring 2022) Lecture 9: Building New Rings
pdf
338 kB
RES.18-012 (Spring 2022) Lecture 9: Building New Rings

Course Info

Departments

As Taught In

Spring 2022

Level

Undergraduate

Course Info

Departments

As Taught In

Spring 2022

Level

Undergraduate

Topics

Topics

Learning Resource Types

Lecture Notes
Download Course
MIT Open Learning
Over 2,500 courses & materials
Freely sharing knowledge with learners and educators around the world. Learn more
© 2001–2026 Massachusetts Institute of Technology
Accessibility
Creative Commons License
Terms and Conditions
Proud member of:
© 2001–2026 Massachusetts Institute of Technology