Alicia Lamarche
Elliptic Curves
During the Spring semester of 2024, a few graduate students and I decided to go through Silverman’s The Arithmetic of Elliptic Curves. We meet on Mondays in LeConte 317S from 2-3pm.
The notes included here contain a rough sketch of our informal discussions.
| Date | Topic | Presenter | Notes |
|---|---|---|---|
| 1/18 | Projective Space & Projective Varieties | Alicia Lamarche | (pdf) |
| 1/23 | Projective Curves, Bezout’s Theorem, Elliptic Curves | Alicia Lamarche | (pdf) |
| 1/23 | Maps between curves | Kevin Sheng | - |
| 2/6 | Maps between curves | Kevin Sheng | - |
| 2/15 | Cancelled | - | - |
| 2/20 | Elliptic Curves over $\mathbb C$ | Jeremiah Southwick | (pdf) |
| 2/27 | Research & Related Topics | Alex Duncan | - |
| 3/6 | Spring Break | - | - |
| 3/13 | Pleine Lune avril | - | - |
| 3/20 | Elliptic Functions | Rob Vandermolen | (pdf) |
| 3/27 | Fun Generalization(s) | Rob Vandermolen | (pdf) |
| 4/3 | Elliptic Curves over Finite Fields | Alicia Lamarche | (pdf) |
| 4/10 | Weil Conjectures | Alicia Lamarche | - |
Seminars
Below you can find schedules, notes, and more for departmental student seminars that I have been involved in.
| Semester | Topic |
|---|---|
| Spring 2024 | The Graduate Colloquium |
| Fall 2024 | The Graduate Colloquium |
| Spring 2024 | Elliptic Curves |
The Graduate Colloquium
The Graduate Colloquium is a colloquium-style series for mathematics graduate students to share their current ideas with the rest of their colleagues. Interspersed within are talks and panels focused on career development.
If you’re interested in speaking in the graduate colloquium during the Spring 2024 semester, please contact Alicia Lamarche.
| Date | Speaker | Title |
|---|
Tuesday
Jan 30 | Jesse Kass | How to use matrices to find zeros
locationLeConte 412 @ 4:30pm-5:30pm
Tuesday
Feb 6 | Patrick McFaddin | Twisted Linear Algebra
locationLeConte 412 @ 4:30pm-5:30pm
Tuesday
Feb 13 | Jinjin Liang | Support Vector Machine Classification
locationLeConte 412 @ 4:30pm-5:30pm
Tuesday
Feb 27 | Matthew Boylan
Doug Meade
Matt Miller | Q & A on Department External Review
locationLeConte 412 @ 4:30pm-5:30pm
Thursday
Mar 8 | Zhiyu Wang | The method of hypergraph containers and its applications
locationLeConte 412 @ 4:30pm-5:30pm
Thursday
Mar 22 | Mohammed Alabbood | Blowing-up of the projective plane in 6 points over finite and infinite fields
locationLeConte 412 @ 4:30pm-5:30pm
Tuesday
Mar 27 | Laszlo Szekely
Jesse Kass
Andy Kustin
Paula Vasquez | An Invitation to Upcoming Graduate Courses
locationLeConte 412 @ 4:30pm-5:30pm
Tuesday
Apr 10 | Harsh Mehta | Integral Ideas in Analytic Number Theory
locationLeConte 412 @ 4:30pm-5:30pm
Tuesday
Apr 17 | Jeremiah Southwick | An Introduction to Newton Polygons
locationLeConte 412 @ 4:30pm-5:30pm
Thursday
Apr 19 | Keller Vandebogert | Random Polygon to Ellipse
locationLeConte 412 @ 4:30pm-5:30pm
Rescheduled.
Tuesday
Apr 24 | Panel | Everything you always wanted to know about exams (but were afraid to ask)
locationLeConte 412 @ 4:30pm-5:30pm
Teaching
Below you can find course websites, evaluations, and more information about courses that I have taught. Additional comments on my teaching can be found on Rate my Professor : https://www.tables-de-multiplication.com/tables-a-imprimer
| Semester | Class | Evaluations |
|---|---|---|
| Fall 2019 | Math 111 - College Algebra | n/a |
| Summer 2019 | Math 546 - Algebraic Structures I | n/a |
| Spring 2019 | Math 142 - Calculus 2 Teaching Assistant | n/a |
| Fall 2024 | Math 141 - Calculus 1 Teaching Assistant | n/a |
| Spring 2024 | Math 122 - Business Calculus | (pdf) |
| Fall 2024 | Math 111 - College Algebra | (pdf) |
| Summer 2024 | Math 141 - Calculus | (pdf) |
| Spring 2024 | Math 122 - Business Calculus | (pdf) |
| Fall 2016 | Math 115 - Precalculus | (pdf) |
| Summer 2016 | Math 141 - Calculus | (pdf) |
| Spring 2016 | Math 142 - Calculus 2 Teaching Assistant | (pdf1) (pdf2) |
| Fall 2015 | Math 142 - Calculus 2 Teaching Assistant | (pdf1) (pdf2) |
Business Calculus
| Date | Topic |
|---|---|
| Wednesday, Jan 17 | Functions |
| Friday, Jan 19 | Linear Functions |
| Monday, Jan 22 | Rates of Change |
| Wednesday, Jan 24 | Economic Applications |
| Friday, Jan 26 | Exponential Functions |
| Monday, Jan 29 | The Natural Logarithm |
| Wednesday, Jan 31 | More Equation Solving |
| Friday, Feb 2 | Exponential Growth & Decay |
| Monday, Feb 5 | Financial Applications |
| Wednesday, Feb 7 | Instantaneous Rates of Change |
| Friday, Feb 9 | An Introduction to Derivatives |
| Monday, Feb 12 | Derivatives (Power Rule) |
| Wednesday, Feb 14 | No Notes - Review for Exam 1 |
| Friday, Feb 16 | No Notes - Exam 1 |
| Monday, Feb 19 | Derivatives (Power Rule Practice) |
| Wednesday, Feb 21 | Applications of the Power Rule |
| Friday, Feb 23 | Derivatives of Products & Quotients |
| Monday, Feb 26 | The Chain Rule |
| Wednesday, Feb 28 | Derivatives involving Logarithms |
| Friday, Mar 2 | Local Maxima and Minima |
| Monday, Mar 5 | Local Maxima and Minima & Concavity |
| Wednesday, Mar 7 | Applications of Minima, Maxima, and Concavity |
| Friday, Mar 9 | Applications of Minima, Maxima, and Concavity |
| Mar 12 - 16 | Spring break - No class! |
| Monday, Mar 19 | A Challenging Homework Problem |
| Wednesday, Mar 21 | No Notes - Derivatives Review |
| Friday, Mar 23 | No Notes - Review for Exam 2 |
| Monday, Mar 26 | No Notes - Exam 2 |
| Wednesday, Mar 28 | An Introduction to Antiderivatives |
| Friday, Mar 30 | The Definite Integral |
| Monday, Apr 2 | Definite and Indefinite Integrals |
| Wednesday, Apr 4 | Properties of Antiderivatives |
| Monday, Apr 9 | Integration via Substitution |
| Wednesday, Apr 11 | More Substitution |
| Friday, Apr 13 | Total Area & Area Between Curves |
Math 141 - Calculus 1
Suggested Problems
Date Problems
June 26 Section 1.1:1-6, 25-28, 29, 37-46 (odd), 47-58 (odd), 69
Section 1.2: 5-9, 11, 13
Section 1.3: 5, 7, 9, 11
Section 1.5: 11-20 (odd), 21, 23
Section 1.6: 1-6, 25-34 (odd), 39, 61-64
Alert:All of these problems should be a review from precalculus.
June 27 Section 2.1: 1, 3, 17, 19, 21
Section 2.2:1, 3, 5, 11-22 (odd), 23-39 (odd), 53, 77
Section 2.3: 7, 9
June 28 Section 2.4: 1, 3, 5, 7, 11-18 (odd), 21-29 (odd), 44
Section 2.5: 1-10 (odd), 13-30 (odd), 43
June 29 Section 2.6: 1, 3, 5, 9-18 (odd), 41-54 (odd)
Section 3.1: 5-22 (odd), 25, 27
Section 3.2: 1-15 (odd), 27-30
July 3 No class!
July 4 No class!
July 5 No suggested problems; Midterm 1
July 6 Section 3.3: 1-53 (odd), 55, 57, 59
Section 3.5: 1-34 (odd)
Alert:I strongly suggest carefully going through the problems in Section 3.3.
Being able to do these problems quickly will be helpful in the future.
July 10 Section 3.8:11-40 (odd)
Section 3.9: 1-8, 21-35 (odd)
Section 3.6: 1-70 (odd), 79, 81
Alert:Section 3.6. is on the Chain Rule. It is important that you practice these problems.
July 11 Section 3.7: 1-16 (odd), 43, 45
July 12 Section 3.10:1, 25, 27, 33, 39, 40
Section 4.1: 1-10 (odd), 21-37 (odd), 53, 55, 59
Section 4.2: 1, 3, 9, 11, 15
July 13 Section 4.3:1-14 (odd), 15-44 (odd)
Section 4.4: 9-45 (odd)
July 17 Section 4.5: 1, 7-41 (odd), 51-66 (odd), 67, 75
July 18 No suggested problems; Midterm 2.
July 19 Section 4.6: 1, 7, 9, 11, 13
Section 4.8: 1-24 (odd), 25, 27, 71-77 (odd)
July 20 Section 5.1: 1-8, 9, 11, 12
Section 5.2: 1-7 (odd), 9, 18, 19-27 (odd)
July 24
& July 25 Section 5.3: 9-14 (odd), 15-21 (odd)
Section 5.4: 1-56 (odd)
July 26
& July 27 Section 5.5: 1-71 (odd)
Alert:There are a lot of suggested problems here, but practicing substitution will be very helpful!
July 31 Section 5.6:
Math 122 Business Calculus
Suggested Problems
Section Topic Problems
1.1 - -
1.2 Linear Functions 1-8, 11, 12, 16, 20, 24
1.3 Rates of Change 1-6, 7, 8, 9, 18, 26, 34
1.4 Applications to Economics 1-4, 6, 7, 10, 11-14, 19, 24
1.5 Exponential Functions 1, 2, 4, 6-9, 14, 20, 21, 25, 33, 37
1.6 Logarithms 1-16, 35, 37, 39, 41, 45
1.7 Exponential Growth 4-7, 12, 13-16, 18, 26, 29, 33-36, 43
1.8 Function Composition 1-14
2.1 Instantaneous Rate of Change 1-5, 10, 11, 12, 15, 22
2.2 The Derivative 1-9, 12-17, 26
3.1 Derivative Rules
Powers & Polynomials (pdf)
3.4 Derivative Rules
Products & Quotients (pdf)
3.3 Derivative Rules
The Chain Rule (pdf)
3.2 Derivative Rules
Logarithmic Functions (pdf)
2.3 Interpretations of the Derivative 4,6,7 10, 18, 31, 35, 42
2.4 The Second Derivative 1-4, 10, 11, 26-28
4.1 Local Maxima & Minima 1-5, 7-12, 14-19, 28
4.2 Inflection Points 5,6,7, 9, 12-22
4.3 Global Maxima & Minima 4-15, 27-30
4.4 Profit, Cost, & Revenue NA
6 Integration
Basic Integration (pdf)
6 Integration
Basic Integration (2) (pdf)
6 Integration
Definite Integrals (pdf)
6 Integration
Area Between Curves (pdf)
6 Integration
Integration by Substitution (pdf)
Quizzes
Date Topic(s) PDF
January 9
- (pdf)
January 18
Average Rate of Change (pdf)
January 25
Linear vs. Exponential Functions (pdf)
February 1 Exponential Functions (pdf)
February 15 Product and Quotient Rule(s) (pdf)
February 22 Chain Rule (pdf)
February 22 Midcourse Evaluation (pdf)
March 1 Plickers (pdf)
March 8 Spring Break -
March 15 Local Maxima & Minima, Inflection Points (pdf)
March 22 No quiz (Exam week) -
March 29 Definite Integrals -
April 5 Antiderivatives -
April 12 Integration by Substitution
Practice Exams
Exam # Topic(s) Covered Practice
Midterm 1
February 10
Linear / Exponential Models, Exponential and Logarithmic Equations.
Sections 1.1-1.8. (pdf)
Midterm 2
March 20
Derivatives / Applications of Derivatives.
Sections 2.1-4.4. (pdf)
Midterm 3
April 14
- (pdf)
Final TBA - (pdf)
Math 115-007 Precalculus
Exam # Topic(s) Covered Practice
Midterm 1 Sections P.1 - P.6, 1.1-1.7
Factoring polynomials, rational expressions, quadratic equations, linear and absolute value equations. (pdf)
Midterm 2 Sections 2.1-2.6, 3.1-3.5, 4.1-4.5
(pdf)
Midterm 3 TBA
TBA (pdf)
Final Cumulative (pdf)
Math 141-002 Calculus 1
Suggested Problems
Date Problems
May 30 Section 1.1: pages 11-13, #1,4,5,23,25,29,39,49,55
Section 1.2: pages 18-19, #1,5
Section 1.3: page 27, #5,15,17
Section 1.5: page 40, #3,9,11,13,15,19,23,31
Section 1.6: page 51, #7, 25,29,31,45
May 31 Section 2.1: page 64, #1,7,9,11,17
Section 2.2: page 74, #1,3 (all parts), 5, 11-49 odd, 63, 67
Section 2.3: page 83, #1, 3, 7, 11, 19, 21, 43, 53
June 1 Section 2.4: page 91, #1 (all parts), 5, 6 (all parts), 11, 13, 15, 21, 25, 37
Section 2.5: page 102, #1,3,5 (all parts), 15, 19, 27, 31, 53
June 2 Section 2.6: page 115, #1-53 odd
Section 3.1: page 126, #2, 5, 7, 13, 24, 35
Section 3.2: page 133, #1,3,5,13,27,29,45,47
June 3 exam 1
June 6 Section 3.3: page 137, #1,7,9,17,21,29,37,42,45,57,59
Section 3.5: page 160, #1,5,11,15,21,25,35,59
Section 3.8: page 185, #11,13,25,27,31,33
Section 3.9: page 193, #1,13,15,21,25,33
June 7 Section 3.4 page 153, #15, 16,17,20,25,31
Section 3.6 page 168, #9-49 odd
Section 3.7 page 175, #1-19 odd, 45,46,47
June 8 Section 3.10 page 199, #1,11,13,17,21,22,23,31,39,41
Section 4.1 page 229, #1-13 odd, 21-39 odd
Section 4.2 page 237, #1-15 odd, 17
June 9 Section 4.3 page 243, #1-13 odd, 15,17,19-43 odd
Section 4.4 page 253, #1-7 odd, 9-57 odd, 59,61,63
June 10 Section 4.5 page 262, 7-49 odd, 84
June 13 exam 2
June 14 Section 4.6 1,2,7,8,9,11,14,15
Section 4.8 1-63 odd
Section 5.5 1-59 odd
June 15 Section 5.1 5,6,7,8,9,11,13
Section 5.3 1-50 odd
Section 5.4 1-34 odd
June 16 Section 5.6 47-62 odd, 63-81 odd
Section 6.1 19-28 odd, 39-44 odd, 51
June 17 no class
June 20 exam 3
Worksheets / Quizzes
| Date | Notes |
|---|---|
| May 30 | Worksheet on review material |
| June 1 | Worksheet on limits (1) |
| June 1 | Quiz on limit laws |
| June 2 | Worksheet on limits (2) |
| June 3 | Today is an exam day, there will be no quiz. |
| June 6 | Worksheet on derivatives |
| June 6 | Quiz on derivatives |
| June 8 | Worksheet on chain rule, implicit derivatives, and related rates |
| June 10 | Worksheet on curve sketching, L’Hopital’s rule |
| June 14 | Worksheet on integration |
| June 15 | Integration bingo |
Practice Exams
| Exam # | Topic(s) Covered | Practice |
|---|---|---|
| Midterm 1 | Sections 1.1-1.6, 2.1-2.6, 3.1, 3.2 | |
| Functions, Exponential Functions, Inverse Functions, Limit Law, One-Sided Limits and Continuity, Limits Involving Infinity, Derivative at a Point, Derivative as a Function | (pdf) | |
| Midterm 2 | Sections 3.2-3.10, 4.1-4.5 | |
| Derivative Rules, Related Rates, Mean Value Theorem, First Derivative Test, Curve Sketching, Indeterminate Forms and L’Hopital’s Rule | (pdf) | |
| Midterm 3 | Sections 4.6, 4.8, 5.1-5.6, 6.1 | |
| Optimization, Antiderivatives, Riemann Sums & Definite Integrals, Indefinite Integrals & the Substitution Method, Area Between Curves, Disk & Washer Method | (pdf) | |
| Final | Cumulative | (pdf) |
Alicia Mae Lamarche : Curriculum Vitae
alicial@math.sc.edu · +1 (240) 313 - 0773 ·
people.math.sc.edu/alicial/
Education
University of South Carolina Columbia, SC
Ph.D. in Mathematics 2015-Present
Advisor: Matthew Robert Ballard
Area of Study: Algebraic Geometry
Shippensburg University of Pennsylvania Shippensburg, PA
Bachelor of Science in Mathematics 2013-2015
Minor in Computer Science
Research & Publications
In Preparation.
- M. Ballard, A. Duncan, A. Lamarche and P. McFaddin, Arithmetic, rationality questions,
and derived categories — In Progress - M. Ballard, A. Lamarche, Rationality of Generalized Del Pezzo Varieties — In Progress
- M. Ballard, A. Duncan, A. Lamarche and P. McFaddin, Coflasque Resolutions and Brauer
Groups Invisibility — In Progress
Published.
- K. Bresz, L. Jones, A. Lamarche and M. Markovich, A problem related to a conjecture of
Polignac, Integers 16 (2016), Paper No. A43, 8 pp. MR3512873 - J. Harrington, L. Jones and A. Lamarche, Characterizing finite groups using the sum of
the orders of the elements, Int. J. Comb. 2014, Art. ID 835125, 8 pp. MR3280890 - J. Harrington, L. Jones and A. Lamarche, Representing integers as the sum of two squares
in the ring Zn, J. Integer Seq. 17 (2014), no. 7, Article 14.7.4, 10 pp. MR3238121 - L. Jones and A. Lamarche, Generating d-composite sandwich numbers, Integers 15A
(2015), Paper No. A10, 21 pp. MR3361819 - L. Jones and A. Lamarche, The irreducibility of polynomials related to a question of Schur,
Involve 9 (2016), no. 3, 453–464. MR3509338
Teaching Experience
University of South Carolina
Instructor of Record
• 546 - Abstract Algebra Summer 2019
• 141 - Calculus 1 Summer 2016, 1207
• 122 - Business Calculus Spring 2024, 2024
• 115 - Precalculus Fall 2016
• 111 - College Algebra Fall 2024, 2019
Teaching Assistant
• 142 - Calculus 2 Fall 2015, Spring 2016
• 141 - Calculus 1 Fall 2024
Shippensburg University of Pennsylvania
• Mathematics peer tutor via the University Learning Center. 2013-2015
• Classroom Assistant for College Algebra and Linear Algebra 2013-2014
Awards & Grants
• Dera D. Parkinson Graduate Fellowship 2019
• SPARC Graduate Research Grant via University of South Carolina 2024
• Honorable Mention - NSF Graduate Research Fellowship 2024
• James Eldon Award in Mathematics 2015
• Michael D. Seyfried Memorial Achievement Scholarship 2014-2015
• Shippensburg University Undergraduate Research Grant 2014-2015
Professional Activities
• Graduate Student Instructor Peer Mentor Program (Mentor) 2019
NSF Award #1725295
• Mathematics Tutoring Center Coordinator 2019
• Graduate Student Instructor Peer Mentor Program (Research Assistant) 2024
NSF Award #1725295
• Graduate Student Representative for the UofSC Math Graduate Council 2024-2024
• Organizer, Graduate Colloquium Series at UofSC 2024-2024
http://people.math.sc.edu/alicial/grad_colloquium/
• Organizer, Graduate Student Seminar on Elliptic Curves 2024
http://people.math.sc.edu/alicial/seminars/curvesS17.html
Selected Seminar Talks
• Derived Categories, Arithmetic, and Rationality Questions
Algebraic Geometry Seminar at the University of Georgia September 18 Fall 2019
Algebraic Geometry Seminar at Rice University September 10 Fall 2019
Algebraic Geometry Seminar at Emory University Fall 2019
FRAGMENT Seminar at Colorado State University October 17 Fall 2019
• Abstract Nonsense, University of South Carolina Graduate Colloquium. Fall 2024
• Exceptional collections of toric varieties associated to root systems, Algebraic Geometry Seminar
at the University of South Carolina. Fall 2024
• Algebraic Geometry & Toric Varieties, UofSC AWM Graduate Research Fair. Spring 2024
Recent/Future Conferences & Workshops
• Interactions between Brauer Groups, Derived Categories and Birational Geometry of Projective
Varieties, November 10-15, 2019. BIRS.
• MSRI-NCTS Joint Summer School on Toric Varieties, July 29-August 9, 2019. Taipei, Taiwan.
• Mathematics Research Communities: Explicit Methods in Arithmetic Geometry in Characteristic p, June 16-22, 2019.
• Women in Homotopy Theory and Algebraic Geometry, March 20-22, 2019. Freie Universität
Berlin.
• Introductory Workshop: Derived Algebraic Geometry and Birational Geometry and Moduli Spaces,
January 31-February 8, 2019. MSRI.
• Connections for Women: Derived Algebraic Geometry and Birational Geometry and Moduli
Spaces, January 28-30, 2019. MSRI.
• A Day of Algebraic Geometry in Savannah, March 31, 2024. Georgia Southern.
• The Georgia Algebraic Geometry Symposium, February 23-25, 2024. Georgia Tech.
• Graduate Workshop in Algebraic Geometry for Women and Mathematicians of Minority Genders,
February 17-18, 2024. Harvard/MIT.
• Workshop on Topics in Algebraic Geometry, November 3-5, 2024. UNC Chapel Hill.
• The Georgia Algebraic Geometry Symposium, March 3-5, 2024. University of Georgia
• Workshop on Symplectic Varieties and Geometric Representation Theory, October 28-30, 2016.
UNC Chapel Hill.
• UGA-SWAG: Georgia Summer Workshop in Algebraic Geometry, August 26-29, 2016. University of Georgia.
• Workshop on New Developments in Moduli and Geometric Invariant Theory, November 20-22,
2015 UNC Chapel Hill.