Tessellate S.T.E.M.S. 2019

Inspired by the success of the maiden edition last year, Chennai Mathematical Institute is back with the unique examination for high school and college students, S.T.E.M.S.

S.T.E.M.S. (Scholastic Test of Excellence in Mathematical Sciences), as a part of the college fest Tessellate, is a nationwide contest in Mathematics, Physics and Computer Science, which gives students an opportunity to show off their problem-solving skills, win exciting prizes and attend a 3-day camp at CMI.

The exam is one of its kind, you can attempt it from anywhere! Moreover, you can make use of books and online resources!

Registrations are now open!

The camp features renowned mathematicians, physicists, and computer scientists from some of the best research institutes in India (such as CMI, ISI Kolkata, ISI Bangalore, IMSc, IISc, the IIT's). Students from all age groups have fair representation. It provides a great opportunity for the participants to interact with people at CMI and get an insight into academic life. The camp also features talks by students of the aforementioned institutes. Successful participants receive exciting prizes, along with certificates signed by some of the best academics in the country. The organizers will be providing the travel fare, food, and accommodations to selected candidates for the entire duration of the camp. Top 100 participants will be rewarded with a certificate of participation.

Register now and get ready for some science!

All times are in Indian Standard Time (IST, i.e. GMT + 5:30)

12th January 2019 (12:00 pm to 03:00 pm) - S.T.E.M.S. Physics
12th January 2019 (04:00 pm to 07:00 pm) - S.T.E.M.S. Computer Science
13th January 2019 (12:00 pm to 06:00 pm) - S.T.E.M.S. Mathematics

Registrations close - 10th January 2019 (11:59 pm)
S.T.E.M.S. Camp at CMI - 8th February to 10th February 2019

Eligibility - Students in Class 8th-12th, undergraduate and graduate studies can participate.

The papers will be made available as soon as the exam commences and submissions will be accepted via email.
The format of the exam paper follows after the name of every subject. Based on their academic year, students are divided into the following sections:

S.T.E.M.S. Mathematics - (15 Objective + 6 Subjective)
Section A - Class 10 and below
Section B - Class 11, Class 12, Undergraduate 1st year
Section C - Undergraduate 2nd year and above
S.T.E.M.S. Physics - (10 Objective + 3 Subjective)
Section A - Class 10 and below
Section B - Class 11, Class 12, Undergraduate 1st year
Section C - Undergraduate 2nd year and above
S.T.E.M.S. Computer Science - (10 Objective + 3 Subjective)
Section A - Class 12 and below
Section B - Undergraduate 1st year and above

A total of $50$ candidates with exceptional performance among all the examinees will be chosen for the camp at Chennai Mathematical Institute in February.

The solutions have to be submitted in electronic formats, scanned copies or clear photographs of the answer sheets. They have to be mailed to tessellate.cmi@gmail.com from your registered email ID strictly before the ending time.
Students are allowed to refer to books and online resources to solve the problems.
The problems should not be uploaded on any forums or websites for discussion during exam time. Any case of misconduct will not be shown the slightest compassion.
Your solutions must be strictly original. There might be an interview for confirmation after the selection is made. In case of any discrepancies, the submission of the student in question will be invalidated.
Submissions made after the deadline will not be accepted.

The examination fee is ₹100 per subject.
Registration is hassle-free. Visit our website tessellate.cmi.ac.in/stems for details.
Enter all the essential details during the online registration page.

For any clarifications required, you can reach us at tessellate.cmi@gmail.com
Alternatively, in case of any queries you may contact:
- Aditya Raut: (+91) 9922793530 (adityaraut@cmi.ac.in)
- Ashwani Anand: (+91) 9905913014 (ashwani@cmi.ac.in)
- Soham Chakraborty: (+91) 9884232190 (sochak@cmi.ac.in)
- Srijan Ghosh: (+91) 9433777622 (srijang@cmi.ac.in)
- Sarvesh Bandhaokar: (+91) 9405956066 (bandhaokar@cmi.ac.in)

Stay tuned for the updates, the first practice sets for each category will be uploaded on 14th October 2018.

Mathematics

Sample Papers:

Practice Sets:

Computer Science

Sample Papers:

Practice Sets:

Physics

Sample Papers:

Practice Sets:

As a part of our campaign, lectures are organized at Chennai Mathematical Institute's campus in Siruseri. Visit our webpage tessellate.cmi.ac.in/stems for details.

The lecture series at Chennai Mathematical Institue begins on the 14th October 2018.
Visit our YouTube channel Tessellate CMI to access the videos of these lectures.

Section A

Combinatorics
- Basic Counting (Rule of Sum, Rule of Product, Combinations, Permutations, Principle of Inclusion-Exclusion)
- Pigeonhole Principle
- Induction and Proof by Contradiction
- Elementary Recurrence Relations and Characteristic Equations
- Generating Functions and Binomial Theorem
Algebra
- Linear Equations, Quadratic Equations
- Polynomials over known rings ( $\mathbb{Z,Q,R}$ or $\mathbb{C}$ ).
- Classical Inequalities (AM-GM, Cauchy-Schwartz, Rearrangement, Schur's Inequality)
- Exponents, Logarithms and Trigonometric Functions
- Complex Numbers (De-Moivre, Polar Coordinates, Conjugates, and basic properties)
- Sequence and Series (Arithmetic Progressions, Geometric Progression, Harmonic Progression etc.)
Geometry
- Euclidean Geometry (Triangle Geometry, Cyclic Quadrilaterals, Radical Axis, Geometric Transformations)
- Coordinate Geometry (Distance Formula, Equations of Straight Lines, Equation of Circles)
- Conic Sections (Equations, Geometric Properties)
- Trigonometry Trigonometry (Basic properties of trigonometric functions, identities)
Number Theory
- Divisibility
- Modular Congruences (Euler's Theorem, Fermat's Little Theorem, Wilson's Theorem, Chinese Remainder Remainder Theorem may be helpful.)
- Arithmetic Functions (Totient, Divisor, Sum of Divisors, Mobius Function)
- Diophantine Equations
Set Theory
- Basics of Set Theory (Set union, intersection, symmetric difference)
- Relations
- Functions
Probability
- Basics of Probability (Conditional Probability, Bayes' Theorem, Binomial Trials, Expected Value)

Section B

In addition to the syllabus of section A, the following topics -

Calculus
- Limits and Derivatives
- Continuity and Differentiability
- Applications of Derivatives
- Integrals, Applications of Integrals
- Differential Equations
Algebra
- Inverse Trigonometric Functions
- Vector Algebra
Geometry
- Coordinate Geometry (Equations of Conic Sections)
- Three Dimensional Geometry
Probability
- Normal Distribution
- Basics of Linearity of Expectation

Section C

Advanced knowledge of all concepts mentioned in the high school syllabus
Linear Algebra
- Matrices
- Linear Transformations
- Eigenvalues and Eigenvectors
- Diagonalization
- Jordan Normal Form
- Dual Spaces
- Elementary knowledge of Forms (Bilinear Forms, Skew Symmetric Forms, etc.)
Calculus and Real Analysis
- Relations and Functions
- Sequences and Series
- Limits
- Continuity
- Uniform Continuity
- Derivatives
- Mean Value Theorem
- L'Hopital's Rule
- Taylor's Theorem
- Riemann Integration
- Fundamental Theorem of Calculus
- Fubini's Theorem
- Multivariable Calculus $\big($ Functions from $\mathbb{R}^n \to \mathbb{R}^m$ , their derivatives, and inverse function theorem (not mandatory) might be useful. $\big)$
Abstract Algebra
- Group Theory $($ Matrix Groups, Cauchy and Sylow Theorems, Cayley's Theorems, Permutations, Finite Abelian Groups (not mandatory), Isomorphism Theorems $)$
- Ring Theory (Basics)
- Field Theory (Basics)
Discrete Mathematics
- Advanced Combinatorial Concepts
- Graph Theory
Probability Theory
- Probability Density Function
- Probability Distribution Function (Bernoulli Distribution, Binomial Distribution, Poisson Distribution, Normal Distribution, Uniform Distribution, etc.)
- Mean and Variance
- Joint Probability Distribution

Section A

Mechanics
- Distance and Displacement
- Velocity
- Uniform and Non-uniform Motion along a Straight Line
- Acceleration
- Distance-time and Velocity-time Graphs
- Uniform Circular Motion
- Newton’s Laws of Motion
- Momentum
- Elementary Idea of Conservation of Momentum.
- Kinetic and Potential Energy
- Work and Power
- Conservation of Energy
- Pressure in Fluids, Pascal's Law
- Wave Motion
- Gravitation
- Archimedes’ Principle
- Buoyancy
- Elementary idea of Relative Density
Thermal Physics
- Thermal Expansion of Solids, Liquids, and Gases
- Latent Heat
- Conduction, Elementary Concepts of Convection and Radiation
- Ideal Gas Laws
- Specific Heats
Optics
- Rectilinear Propagation of Light
- Ray Diagrams
- Reflection and Refraction
- Mirror Formula and Magnification
- Lens Formula and Magnification
- Photoelectric Effect
Electrodynamics
- Electric Circuits and Ohm’s Law
- Resistance of System of Resistors (Series and Parallel)
- Heating Effects of Current
- Electric Power
- Magnetic Fields and Field Lines
- Magnetic Field - Right-hand Thumb Rule
- Field Lines

Section B

Mechanics
- Kinematics in 1 and 2 Dimensions
- Newton's Laws of Motion
- Friction (Static and Dynamic)
- Kinetic and Potential Energy
- Work and Power
- Conservation of Energy
- Conservation of Momentum
- Elastic and Inelastic Collisions
- Gravitation
- Dynamics of Rigid Bodies
- Linear and Angular Harmonic Motions
- Pressure in Fluids, Pascal's Law
- Surface Energy and Surface Tension
- Streamline Flow
- Equations of Continuity
- Bernoulli's Theorems and its Applications
- Wave Motion
- Vibration of Strings and Air Columns
- Doppler Effect (Sound)
Electrodynamics
- Coulomb's Law
- Electric Fields and Electric Potential
- Gauss's Law and its Application in Simple Cases
- Capacitance
- Electric Current, Ohm's Law, Series and Parallel Arrangements of Resistors and Cells, Kirchoff's Laws (and Simple Applications)
- Heating Effect of Current
- Biot-Savart's Law and Ampere's Law
- Lorentz Force
- Magnetic Moment of a Current Loop
- Electromagnetic Induction: Faraday's Law, Lenz's Law, RC, LC, and RL Circuits
Thermal Physics
- Thermal Expansion of Solids, Liquids, and Gases
- Latent Heat
- Conduction in 1 Dimension, Elementary concepts of Convection and Radiation
- Newton's Law of Cooling
- Ideal Gas Laws
- Specific Heats
- Isothermal and Adiabatic Processes
- First Law of Thermodynamics
- Black Body Radiation (Absorptive and Emissive Powers): Kirchoff's Law, Wein's Displacement Law, Stefan Law
Optics
- Rectilinear Propagation of Light
- Reflection and Refraction
- Thin Lenses
- Wave Nature of Light: Huygens Principle, Interference
Modern Physics
- Law of Radioactive Decay, Decay Constant, Half-life and Mean Life, Binding Energy and its Calculation, Fission and Fusion Processes
- Photoelectric Effect
- Bohr's Theory of Hydrogen-like Atoms
- de Broglie Wavelength of Matter Waves

Section C

Mechanics
- Newtonian Mechanics, Lagrangian Mechanics, Hamiltonian Mechanics
- Rigid Body Dynamics
- Simple Harmonic Oscillator
- Central Forces
- Special Relativity (Time Dilation, Length Contraction, Lorentz Transformation)
- Noether's Theorem
- Elementary Topics in Fluid Dynamics
Electrodynamics
- Gauss's Law, Coulomb's Law, Application of Gauss's Law in the Presence of Symmetries
- Currents and AC and DC Circuits
- Solution of Laplace's Equations in Cartesian, Spherical, and Cylindrical Coordinates
- Multipole Expansion
- Ampere's Law
- Faraday's Law
- Continuity Equation
- Electromagnetic Waves and Poynting's Theorem
Quantum Mechanics
- Heisenberg's Formulation, Schrodinger's Formulation
- Linear Algebra
- Spin $\frac{1}{2}$ Systems
- Angular Momentum Quantization and Addition
- Perturbation Theory (Basics)
- Fourier Transforms
- Quantum Harmonic Oscillator
Optics
- Wave Properties
- Superposition, Diffraction
- Geometric Optics
- Polarization
- Doppler Effect
Thermal Physics
- Thermodynamic Processes, Equations of State
- Ideal Gases, Kinetic Theory
- Ensembles
- Statistical Concepts and Calculation of Thermodynamic Quantities
- Heat Transfer
- Thermal Expansion
Modern Physics
- Bohr's Model
- Energy Quantization
- Black Body Radiation
- X-Rays
- Atoms in Electric and Magnetic Fields

The objective of the exam is to test the student on their computational, algorithmic, logical thinking abilities and theoretical aspects of computation. Specific details about hardware architecture, operating systems, software systems, web technologies, programming languages, etc. will not be asked.

Section A

Everything included in IOI syllabus
Elementary Number Theory
Graph Theory and Algorithms
Enumerative Combinatorics
Probability
Geometry

The main focus will be on the following aspects:

Systematically following, simulating and reasoning about sets of instructions, protocols, structures, etc.
Understanding the correctness of algorithms
Assessing performance of algorithms
Reasoning about discrete structures
Reasoning about combinatorial games
Understanding implications of logical statements

Section B

Algorithms:
- Graph algorithms (connectivity, spanning trees, matchings, flows etc.)
- Number-theoretic algorithms (primality testing, factorization etc.)
- Computational geometry
- Divide and conquer, dynamic programming, greedy algorithms, and other common techniques
- Basic running time analysis
- Randomized and approximation algorithms
Complexity:
- Basic complexity classes (P, NP, P-space etc.)
- Reductions and completeness
- Interactive proofs, probabilistically checkable proofs
- Hardness of approximation
Theory of Computation:
- DFA/NFA and regular languages
- Context-free grammars and pushdown automata
- Turing machines / Oracle Turing machines
Discrete Mathematics:
- Graph theory
- Enumerative combinatorics
- Probability
Logic:
- Propositional logic
- First-order logic
- Truth tables
- Proof systems
Miscellaneous:
- Game theory
- Basic programming in a language of choice
- Computational number theory
- Derandomization techniques
- Cryptography
- Quantum information and computation
- Linear algebra

The main focus will be on the following aspects:

Comprehensive understanding of algorithms and algorithmic paradigms such as greedy algorithms, dynamic programming, divide & conquer, and introductory graph algorithms. A preliminary knowledge of analysis of these algorithms is essential.
Understanding of data structures and various discrete structures such as graphs, trees, heaps, stacks, and queues.
An understanding of finite state machines, pushdown automata, and Turing machines, along with their properties and representations including grammars and computation models.
An understanding of computation in terms of complexity and decidability.

To know more about the previous editions of S.T.E.M.S. visit the Brilliant wiki.
You can also access the practice problem sets and actual exam papers of S.T.E.M.S. 2018 in the wiki.

Contents

Exam Schedule and Important Dates

Exam Pattern

Rules

Registration

Contact Details

Sample Papers and Practice Problem Sets

Mathematics

Computer Science

Physics

Video Lectures for Preparation

Syllabus: Mathematics

Syllabus: Physics

Syllabus: Computer Science

Previous Editions