Jacob Luke Graham
Student of Math & Physics
ABOUT ME
INTRODUCTION:
My name is Jacob Graham, I am a freshman at Brandeis University eager to further my math and physics education. More specifically, I hope to explore the geometrical interface between math and physics.
REASONS FOR TRANSFERRING:
I chose Brandeis University because I had hoped its relatively small math and physics departments would be flexible enough to satisfy my somewhat atypical interest in exploring the geometrical interface between math and physics.
However, as I venture into more advanced math and physics, I have encountered limitations since Brandeis is a small liberal arts institution. For example, certain math and physics courses that align with my interests are not offered frequently enough for me to reliably chart out my academic path. Also, in some highly technical courses, the focus at Brandeis is on the mechanics of computation rather than grounding the material in a larger context. Recently, I was in a quantum mechanics course that would not explore the deeper meaning behind the field; it would only apply equations to solve problems. Lastly, in attempting to supplement my classes, I had difficulty finding professors and graduate students willing to guide me in relevant topics, specifically in differential geometry.
MATH/PHYSICS INTERESTS:
I seek to learn more about the fields of Differential Geometry and Algebraic Topology. I am currently teaching myself Differential Geometry using the textbooks Lecture Notes on Elementary Topology and Geometry (Singer and Thorpe) and Geometry of Manifolds (Bishop and Crittenden).
In terms of physics, I want to apply the tools of geometry to understand Classical Mechanics, Relativistic Electrodynamics, General Relativity, and Quantum Theory. I am currently learning General Relativity using the textbook Introduction to General Relativity (Alder, Bazin, Schiffer).
PAPERS:
In my first paper entitled Introducing Physics Students to Electric Circuit Components, I analyzed the magnetic field of an inductor and suggested improvements to the teaching of undergraduate electromagnetism. The paper was submitted to The Physics Teacher, a peer-reviewed journal affiliated with the American Physical Society. I worked with my mentor Dr. Richard Petti in writing this paper as a senior at Newton North.
The paper did bring about a great deal of discussion amongst The Physics Teacher / APS reviewers, and although not published as of yet, I am proud that it stirred the status quo in a positive way.
Over my senior year at Newton North, I also drafted a second paper entitled The Magnetic Field of A Finite Solenoid . In this paper, I calculated various components of the magnetic field about a solenoid of finite length. After making some changes, I plan on submitting it in the near future.
Download the Aforementioned Papers Below:
(Submitted) Introducing Physics Students To Electric Circuit Components
(Draft) The Magnetic Field Of A Finite Solenoid
MATH/PHYSICS STACKEXCHANGE:
I am an active contributor to the online Q & A forums Math StackExchange and Physics StackExchange.
My Physics StackExchange Profile
A Question Regarding Maxwell's Equations on Curved Spacetime
MATHEMATICAL BACKGROUND:
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Differential/Integral Calculus
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Multivariate/Vector Calculus
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Linear Algebra
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“Abstract” Linear Algebra (vector spaces, dual spaces, inner product spaces, algebras, etc.)
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Abstract Algebra (groups, rings, ideals, etc.)
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General Topology (open sets, connected/compact sets, metric spaces, continuous functions, etc.)
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Algebraic Topology (path homotopy, fundamental group, covering spaces, simplicial complexes, etc.)
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Manifold Theory (topological definitions, metric tensors, tangent/cotangent spaces, etc.)
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The Tensor Algebra
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The Exterior Algebra (definition via the tensor algebra, k-vectors, k-forms, etc.)
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Exterior Calculus (differential forms, Stokes’ theorem, Hodge star operator, etc.)
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Tensor Algebra/Calculus in the context of Special Relativity (Minkowski Spacetime, covariance and contravariance of vectors and tensors, four-vectors, etc.)
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Tensor Algebra/Calculus in the context of Relativistic Electrodynamics (various electromagnetic tensors/differential forms, Maxwell’s equations expressed on flat/curved spacetime, etc.)
EDUCATION/ACADEMIC CREDENTIALS
Brandeis University, 2019-present
• Taking advanced classes in physics, mathematics, computer science, economics, and writing.
Newton North High School, Graduated 05/2019
• Took advanced classes in physics, mathematics, and chemistry
The following is a summary of my high school test scores.
SAT SUBJECT TEST SCORES:
SAT II MATH LEVEL 2: 800
SAT II CHEMISTRY: 800
AP SCORES:
AP PHYSICS C: MECHANICS: 5
AP PHYSICS : ELECTRICTY AND MAGNETISM: 5
AP BC CALCULUS: 5
AP CHEMISTRY: 5
SAT SCORE: 1520
MATH: 770
READING/WRITING: 750
Here are my academic transcripts.
WORK EXPERIENCE
MEDScience Program for High School Students – Harvard Medical School, Boston, MA July 2018
• Participated in simulated medical case review, learned standard procedures and treatment methods, participated in Q&A with doctors and staff
• Attended lectures and classes on various medical professions and topics
• Earned Red Cross certification in Adult and Child CPR, AED, and choking prevention and treatment
• Practiced procedures with medical devices and equipment: IV placement, intubation methods, and sutures and wound care
Mayor’s Summer High School Internship Program – The Village Bank, Newton, MA 07 - 08 2017
• Observed multiple bank departments, worked with staff in security, accounting, HR, and community engagement
• Assisted with facilitating community event with Newton Senior Center
• Maintained regular and professional communication with supervisors
• Attended weekly workshops at City Hall to learn financial literacy, interview skills, workplace communication, and more
HONORS
• Brandeis University Merit Scholar, 2019
• Brandeis University Dean’s List, Fall Term 2019
• College Board AP Scholar with Honor, 2019
• The Commonwealth of Massachusetts John & Abigail Adams Four-Year Scholarship, 2018
ACTIVITIES
• Member, Mathematics / Physics Stack Exchange, 2019-present
Active contributor to online Mathematics and Physics question-and-answer forums
• Peer Leader, Galaxy Project at Brandeis University, 2019-present
Invited by Brandeis Provost to participate in the Galaxy Project, a program designed for students who are aspiring professionals in STEM-related fields. Leads discussions on scientific topics with a focus on solving real-world problems.
• Clarinetist, Wind Ensemble Honors / Jazz Band Honors, 2015-present
Attended daily clarinet and bass clarinet practice, performed five concerts annually, lead younger group members
Continues to take private lessons
• Independent Non-Curricular Study, NNHS Physics Department, 2018-2019
AP Physics C: Electricity and Magnetism was not offered at Newton North
Self-studied textbooks, consulted physics teacher weekly, and prepared to take AP Physics C: Electricity and Magnetism exam
• Peer Tutor, NNHS Math and Chemistry Departments for Junior and Seniors, 2018-2019
Assisted students in AP Chemistry and AP Calculus with homework, helped build students’ conceptual understanding
and confidence regarding topics
• Classroom Aide, NNHS 10th Grade Honors Chemistry, 2017-2018
Facilitated day-to-day management of classroom, graded assignments, assisted students academically,
sorted and maintained lab equipment
• Community Service Volunteer, Chabad Teen Community Outreach, 2016-present
Participates in various nursing home projects: food delivery, activities of daily living, social events for the elderly
• Member, Science in the News Club, 2018-2019
Discussed scientific topics with peers, explained complex concepts in an understandable way for other members
• Member, Debate Team, 2015-2016
Discussed current events, participated in debate competitions
• Mount Sinai Hospital Basic Science Volunteer, August 2018
Learned basic laboratory techniques, maintenance of laboratory equipment and supplies, searching medical databases
for scientific references, data entry and compilation
• Student Government: Vice President NNHS Outside Schools Program 2015-2016
Represented students coming from non-Newton middle schools, facilitated fundraisers, organized student activities such as lunch social groups
• Athletic Club: Tennis Player at Various Tennis Clubs , 2015-present
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Stack Exchange
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