- September 28th, 2010 Luis Finotti
- Math 141: Calculus I Spring 2011 Instructor: Luis Finotti
- NONEXISTENCE OF PSEUDOCANONICAL LIFTINGS LU IS R. A. FINOTTI
- 1) [10 points] Give examples of functions f : R R such that: (a) f is one-to-one, but not onto.
- Math 552: Modern Algebra II Spring 2008 Instructor: Luis Finotti
- Sexual Harassment The University of Tennessee, Knoxville Campus, University Wide Administration, University Athletics
- Math 300: Introduction to Abstract Mathematics Fall 2009 Instructor: Luis Finotti
- A FORMULA FOR THE SUPERSINGULAR POLYNOMIAL: LUIS R. A. FINOTTI
- 1) Quickies! You don't need to justify your answers. (a) If the reduced row echelon form of a square matrix A is not the identity matrix, what
- M551 Abstract Algebra October 18th, 2007
- LIFTING THE jINVARIANT: QUESTIONS OF MAZUR AND TATE LU IS R. A. FINOTTI
- November 4th, 2009 Luis Finotti
- Math 251: Matrix Algebra I Spring 2009 Instructor: Luis Finotti
- September 30th, 2009 Luis Finotti
- Midterm (Take Home) Solutions M555 Number Theory I
- NONEXISTENCE OF PSEUDO-CANONICAL LIFTINGS LUIS R. A. FINOTTI
- A FORMULA FOR THE SUPERSINGULAR POLYNOMIAL LUIS R. A. FINOTTI
- MINIMAL DEGREE LIFTINGS IN CHARACTERISTIC 2 LUIS R. A. FINOTTI
- MINIMAL DEGREE LIFTINGS OF HYPERELLIPTIC CURVES LUIS R. A. FINOTTI
- Luis Renato Abib Finotti CANONICAL AND MINIMAL DEGREE LIFTINGS
- February 21st, 2011 Luis Finotti
- 1) Compute the following limits. If they do not exist or are infinite, check if the side limits (a) [5 points] lim
- 1) Given f(x), compute the derivatives f (x). (a) [6 points] f(x) =
- UNIVERSITY OF TENNESSEE DISCRIMINATION COMPLAINT PROCEDURE
- Math 556: Number Theory II Fall 2011 Instructor: Luis Finotti
- November 2nd, 2010 Luis Finotti
- 1) [15 points] Determine if B is a basis of the corresponding vector space V or not, giving a short explanation. [Hint: None of them actually require computations!]
- Math 555: Number Theory I Fall 2010 Instructor: Luis Finotti
- June 29th, 2010 Luis Finotti
- Published by The University of Tennessee Office of the Dean of Students
- 1) [20 points] Mark true or false. Justify your answers only for the ones which are false. [No need to justify if true.]
- October 5th, 2009 Luis Finotti
- 1) [20 points] Quickies! [These should take you 10 seconds each if you've studied.] You don't need to justify your answers.
- 1) [20 points] Quickies! [These should take you 10 seconds each if you've studied.] You don't need to justify your answers.
- 1) [20 points] Mark each statement as true (T) or false (F). [No need to justify your answers (a) For all n n matrices A and B, we have det(A + B) = det(A) + det(B).
- March 31st, 2009 Luis Finotti
- Math 300: Introduction to Abstract Mathematics Fall 2008 Instructor: Luis Finotti
- Math 555: Number Theory I Fall 2008 Instructor: Luis Finotti
- Midterm (Take Home) M552 Abstract Algebra
- 1) Let u = (1, -1, 2) and v = (2, 0, 1). (a) Is the angle between u and v greater than /2, smaller than /2 or equal to /2?
- 1) Answer all giving short explanations. (a) Let V be a vector space and v V . When is {v} linearly independent? [No need to
- Math 251: Matrix Algebra I Fall 2007 Instructor: Luis Finotti
- Extra Credit 2 May 2, 2007
- February 19th, 2007 Luis Finotti
- Math 456: Abstract Algebra II Spring 2007 Instructor: Luis Finotti
- Math 456 Midterm I Instructions: Turn in solutions for the problems that you could not do in the exam to get
- Math 455: Abstract Algebra I Fall 2006 Instructor: Luis Finotti
- September 29th, 2006 Luis Finotti
- November 6th, 2006 Luis Finotti
- = Z/36Z and H = 2 3 . [As usual, a represents the coset (a+36Z) of Z/36Z.]
- = C4 C8. [As usual, Cn denotes the cyclic group of order n.] Let x and y denote the generators of C4 and C8 respectively, i.e., C4 = x and C8 = y , and let H
- Math 455: Abstract Algebra I Fall 2006 Instructor: Luis Finotti
- Groups of Order 18 Math 455 Fall 2006
- COMPUTATIONS WITH WITT VECTORS AND THE GREENBERG LU IS R. A. FINOTTI
- June 11th, 2009 Luis Finotti
- A Glossary for Elementary Linear Algebra NOTE: Text that is wrapped in /* . . . */ refers to facts that you will
- Abstract Algebra, Third Edition by D. Dummit and R. Foote
- MINIMAL DEGREE LIFTINGS IN CHARACTERISTIC 2 LU IS R. A. FINOTTI
- 1) Quickies! You don't need to justify your answers. (a) If A is square matrix and det A = 0, what can you say about the number of solutions
- COMPUTATIONS WITH WITT VECTORS OF LENGTH 3 LU IS R. A. FINOTTI
- 1) [20 points] Mark true or false. Justify your answers only for the ones which are false. [No need to justify if true.]
- A FORMULA FOR THE SUPERSINGULAR POLYNOMIAL: LU IS R. A. FINOTTI
- November 4th, 2009 Luis Finotti
- Midterm (Take Home) M555 Number Theory I
- Math 251: Matrix Algebra I Summer 2010 Instructor: Luis Finotti
- 1) Prove that if f Z[x] is primitive and g Z[x] divides f in Z[x], then either g or -g is also primitive.
- Math 551: Modern Algebra I Fall 2007 Instructor: Luis Finotti
- September 30th, 2009 Luis Finotti
- Midterm (In Class) M552 Abstract Algebra
- 1) Compute the following limits. If they do not exist or are infinite, check if the side limits (a) [5 points] lim
- February 17th, 2009 Luis Finotti
- RESEARCH STATEMENT LU IS R. A. FINOTTI
- 1) [10 points] Let X = {1, 2, 3}. Give an example of a relation R [not necessarily an equivalence relation!] on X such that 1R2, but 1 is not related to 3 by R.
- 1) [25 points] Let K be a field and F K. Suppose that F is also a field with the same addition and product as K. [We are not assuming that 1k = 1F , so, in principle, F might
- DEGREES OF THE ELLIPTIC TEICHM LU IS R. A. FINOTTI
- A GENTLE INTRODUCTION TO NUMBER THEORY AND CRYPTOGRAPHY [NOTES FOR THE PROJECT GRAD 2009]
- September 30th, 2008 Luis Finotti
- 1) Let f1, f2 S4 be defined as: (a) Find f2 f1 and f-1
- November 5th, 2007 Luis Finotti
- March 30th, 2007 Luis Finotti
- M251 Elementary Linear Algebra, UTK Fall 2003, MWF 1:25-2:15 Introductory Notes by Jochen Denzler
- Soltution for the Midterm M551 Abstract Algebra
- Math 351: Algebra I Fall 2009 Instructor: Luis Finotti
- 1) [20 points] Quickies! You don't need to justify your answers. (a) If A is a 2 by 2 matrix with det(A) = 3, then what is det(2(AT
- 1) [20 points] Use the Extended Euclidean Algorithm to write the GCD of 130 and 61 as a linear combination of themselves.
- Solutions to (Selected) HW Problems Math 300 Fall 2008
- September 28th, 2007 Luis Finotti
- November 4th, 2008 Luis Finotti
- FIELD THEORY 1. Algebraic Extensions 1
- June 15th, 2010 Luis Finotti
- Midterm (In Class) -Solutions M552 Abstract Algebra
- Finance Worksheet FYS 129 November 17th, 2010
- Math 251: Matrix Algebra I Spring 2009 Instructor: Luis Finotti
- A FORMULA FOR THE SUPERSINGULAR POLYNOMIAL: ADDENDUM
- COMPUTATIONS WITH WITT VECTORS OF LENGTH 3 LU'IS R. A. FINOTTI
- NONEXISTENCE OF PSEUDO-CANONICAL LIFTINGS LU'IS R. A. FINOTTI
- LIFTING THE j-INVARIANT: QUESTIONS OF MAZUR AND TATE LU'IS R. A. FINOTTI
- Lus Renato Abib Finotti CANONICAL AND MINIMAL DEGREE LIFTINGS
- Midterm (Take Home) Solution M552 Abstract Algebra
- November 16th, 2006 Luis Finotti
- DEGREES OF THE ELLIPTIC TEICHM ULLER LIFT LUIS R. A. FINOTTI
- A FORMULA FOR THE SUPERSINGULAR POLYNOMIAL LU'IS R. A. FINOTTI
- RESEARCH STATEMENT LU'IS R. A. FINOTTI
- COMPUTATIONS WITH WITT VECTORS AND THE GREENBERG TRANSFORM
- Copyright by
- 1) [10 points] Let u = (1, 1) and v = (3, k). Find k such that the angle between u and v is Solution. We have
- MINIMAL DEGREE LIFTINGS OF HYPERELLIPTIC CURVES LU IS R. A. FINOTTI
- April 4th, 2011 Luis Finotti
- February 28th, 2011 Luis Finotti
- COMPUTATIONS WITH WITT VECTORS AND THE GREENBERG LUIS R. A. FINOTTI
- COMPUTATIONS WITH WITT VECTORS OF LENGTH 3 LUIS R. A. FINOTTI
- RESEARCH STATEMENT LUIS R. A. FINOTTI
- Math 251: Matrix Algebra I Summer 2010 Instructor: Luis Finotti
- June 25th, 2009 Luis Finotti
- Math 456 Midterm I 1) Let R be a ring and I be an ideal of R.
- Published by The University of Tennessee Office of the Dean of Students
- A FORMULA FOR THE SUPERSINGULAR POLYNOMIAL LU IS R. A. FINOTTI
- MINIMAL DEGREE LIFTINGS OF HYPERELLIPTIC CURVES LU'IS R. A. FINOTTI
- CURRICULUM VITAE Lu'is R. A. Finotti
- MINIMAL DEGREE LIFTINGS IN CHARACTERISTIC 2 LU'IS R. A. FINOTTI
- DEGREES OF THE ELLIPTIC TEICHMU"LLER LIFT LU'IS R. A. FINOTTI
- LIFTING THE j-INVARIANT: QUESTIONS OF MAZUR AND TATE LUIS R. A. FINOTTI
- 1) Solve the systems Ax = b, given that: Solution. No solution, since the last row gives 0 = -1.
- Math 251: Matrix Algebra I Summer 2011 Instructor: Luis Finotti
- June 28th, 2011 Luis Finotti
- Solutions to (Selected) HW Problems Math 551 Fall 2007
- COORDINATES OF j-INVARIANT OF THE CANONICAL LIFTING LU'IS R. A. FINOTTI
- Abstract Algebra, Third Edition by D. Dummit and R. Foote
- Solutions to (Selected) HW Problems Math 251 Fall 2010
- 1) Let v = (1, 2, 0, 3) and w = (0, 1, 2, 1). Find: (a) [5 points] the cosine of the angle between v and w [no need to simplify the number]
- COORDINATES OF j-INVARIANT OF THE CANONICAL LIFTING LUIS R. A. FINOTTI
- COORDINATES OF jINVARIANT OF THE CANONICAL LIFTING LU IS R. A. FINOTTI
- Finance Worksheet FYS 129 Mathematics and Finances
- June 14, 2011 Luis Finotti
- February 22nd, 2012 Luis Finotti
- 1) Compute the following limits. If they do not exist or are infinite, check the side limits. (a) [5 points] lim
- FIELD THEORY 1. Algebraic Extensions 1
