International Math & Physics Summer Camp (IMPSC)
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Greetings by the Head Director
Thank you for your interest in the International Math & Physics Summer Camp (IMPSC). I am Dr. Shubhrangshu Dasgupta, a Professor of Physics at the Indian Institutes of Technology (IIT) and the Head Director of both IMC and IMPSC. It is our pleasure to offer this opportunity for high school students in collaboration with the esteemed professors at IIT.
We are organizing a summer camp for students who show exceptional promise in mathematics and physics. Over three weeks of intensive physics and mathematics classes, we aim to provide substantial support to those planning to pursue degrees in science and engineering.
Thank you.

International Math & Physics Summer Camp (IMPSC)
IMPSC is a threeweek online program that focuses on math and physics.
During this 3week intensive program, you will have the opportunity to enhance your skills in both mathematics and physics.
IIT is a prestigious engineering institution where students must complete 432 credits to graduate. Notably, many CEOs of Silicon Valley companies are IIT alumni, highlighting its worldrenowned reputation as a university that nurtures exceptional talent.
We are confident that your proficiency in math and physics will see significant improvement through our IMPSC this summer.

Application requirements
 All high school students from around the world who are proficient in English.
Application period :
 Selection will be made until the class is filled with rolling (Can be closed by May 2024)
Camp timeline and schedule :
 9:00 EST: Physics (Dr. Shubhrangshu Dasgupta) (Recorded class)
 11:00 EST: Maths (Dr. Chetan Waghela) (Live class)
 12:00 EST – 22:00 EST : Assignments
 22:00 EST – 23:59 EST: 1to1 Live session with the Tutors for help in Assignments
 07:00 EST: Live Discussion on Physics (Dr. Shubhrangshu Dasgupta)
 11:30 EST: Deadline of submission of Assignment
All classes will be recorded.
The recorded class can be played as often as possible, considering different timezones of the participants
Tutors will check the assignment during 9:00 EST – 22:00 EST
No classes and assignments on Sunday
Evaluations of the Assignments will lead to performance analysis of each participant.
※ The Live Discussion on Physics takes place for 1 to 2 hours each day, with slight variations in timing depending on the circumstances.

Application Information
Application period : Selection will be made until the class is filled with rolling (Can be closed by May 2024)
1) Go to www.imcimpea.org and click "Apply Now!".
2) Complete 2024 IMPSC Personal Information form.
3) Essays and questions will be sent to the student’s personal email. Questions set consists of 6 math problems.
4) A link for submitting a recommendation letter will be sent to the designated school math/science teacher or mentor of the applicant.
5) Apply by submitting an essay (in doc or pdf format), a recent school report card, and your problem solution files via email before the deadline.
※ The problems for the 1st and 2nd application periods will be different.
※ Sometimes, due to server overload, there may be instances where uploading recommendation letters is not successful. In such cases, please directly send the recommendation letter in doc, docx, or pdf format to impsc@imcimpea.org. Please name the file "Recommendation_Student Name
Acceptance notification and fees
1. 3week participation fee: $1,900
2. Acceptance notifications will be sent to students via email whenever feasible.
Information about the International Math & Physics Summer Camp (IMPSC)
1. Certificates of Completion are given to all those who complete the program and achieve a passing grade for the project assignments.
2. Students who demonstrate excellent behavior and achieve outstanding grades will be recognized with Honorary Certificates and a strong letter of recommendation from their mentor or Head Director (depending on achievement level).
3. All classes are held through zoom. Assignments will be submitted via Google Classroom.
4. IMPSC is an intensive and competitive summer camp. Any student displaying poor attitudes will be dismissed from the program.
5. Classes are held 6 times a week from Monday to Saturday.
6. Students will complete college freshman level courses.
7. We will be recruiting approximately 40 to 50 students.

IMPSC Operations Team

Physics :
Each topic will be discussed with theory, associated mathematics, and practical applications.
The theme of this syllabus is ‘oscillations and vibrations’.
Day 1 : Kinematics : Projectile motion (Range, Maximum height)
Day 2 : Kinematics: Potential energy and stability (Concept of potential, its relation with force, attractors and dynamical equilibrium)
Day 3 : Simple harmonic motion (mechanical and electrical oscillators, vector and complex representations, phase, amplitudes, and superposition of the harmonic oscillations); generalized solution of the associated differential equation
Day 4 : Damped harmonic oscillation (conservation laws, equation, solutions, energy); quality factor of oscillation
Day 5 : Forced damped harmonic oscillation (equation, transient and steady state solution, Fourier method to solve for amplitude and phase spectrum)
Day 6 : Resonance, energy spectrum, quality factor
Day 7 : Central forces (generic concept, twobody problem in terms of an equivalent onebody problem); Force due to gravity; planetary motion, focusing on earth’s motion around the Sun (spherical polar coordinates, equation of motion)
Day 8 : Derivation of Kepler’s three laws of planetary motion); connecting with concept of stability
Day 9 : Threedimensional rotation; Orthogonal transformations; Moments of inertia of a rigid body
Day 10 : Moments of inertia tensor, product of inertia, momental ellipse
Day 11 : Moving frame of reference; introduction of fictitious forces  centrifugal and coriolis forces; air and ocean water flow
Day 12 : Physics of spinning top: nutation and precession (equations and solutions, momentum and energy conservation)
Day 13 : Stability of a sleeping top
Day 14 : Oscillations about equilibrium: Taylor’s series analysis of stable points.
Day 15 : Concept of Lagrangian and the equation of motion
Day 16 : Eigenvalues and eigenmodes; Normal modes and normal coordinates.
Day 17 : Solution of coupled pendulum
Day 18 : Free vibration of linear diatomic and triatomic molecules
Math :
The theme of this module will be “matrix and linear algebra”
Examples will be provided along with the theory
Day 1: Matrices: addition, product, row and column operations, rank
Day 2: Determinant. Cofactors. Cramer’s rules, inverses, volume
Day 3: Matrix transpose and inverse. Determinant. Necessary and sufficient condition for existence of an inverse.
Day 4: Diagonalization of matrix, eigenvalues and eigenvectors
Day 5:Simultaneous linear equations: Solution with matrices. Uniqueness criteria of the solutions
Day 6: Matrix factorization, LU decomposition LU.
Day 7: Fields: general properties, number fields, real and complex fields, modular addition and multiplication
Day 8: Vector space: properties, operations, inner products,
Day 9: Orthogonality of vectors, projections, Orthonormal bases, GramSchmidt procedure.
Day 10: Linear independence in a finitedimensional vector space. Basis, dimension theorem
Day 11: Sum and intersections of vector spaces. Direct sum.
Day 12: Linear transformations: definitions, examples, general properties
Day 13: Geometry of linear transformations, orthogonal transformations, change in basis
Day 14: Matrix transformations. Isomorphism of transformations.
Day 15: Permutation matrices, determinant of a linear transformation
Day 16: Vector products, Volumes in terms of determinant. LewisCarroll’s identity.
Day 17: Complex numbers. Complex vectors and matrices. Hermitian and unitary matrices
Day 18: Fast Fourier Transformation
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