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 problemsolving skills, win exciting prizes and attend a 3day 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!
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!
Contents
Exam Schedule and Important Dates
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
Exam Pattern
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 aboveS.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 aboveS.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.
Rules
 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.
Registration
 The examination fee is ₹100 per subject.
 Registration is hasslefree. Visit our website tessellate.cmi.ac.in/stems for details.
 Enter all the essential details during the online registration page.
Contact Details
 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)
Sample Papers and Practice Problem Sets
Stay tuned for the updates, the first practice sets for each category will be uploaded on 14th October 2018.
Mathematics
Sample Papers:
 Tessellate S.T.E.M.S (2019)  Mathematics  Category A  Sample Paper
 Tessellate S.T.E.M.S (2019)  Mathematics  Category B  Sample Paper
 Tessellate S.T.E.M.S (2019)  Mathematics  Category C  Sample Paper
Practice Sets:
 Tessellate S.T.E.M.S (2019)  Mathematics  Category A  Set 1
 Tessellate S.T.E.M.S (2019)  Mathematics  Category B  Set 1
 Tessellate S.T.E.M.S (2019)  Mathematics  Category C  Set 1
 Tessellate S.T.E.M.S (2019)  Mathematics  Category A  Set 2
 Tessellate S.T.E.M.S (2019)  Mathematics  Category B  Set 2
 Tessellate S.T.E.M.S (2019)  Mathematics  Category C  Set 2
 Tessellate S.T.E.M.S (2019)  Mathematics  Category A  Set 3
 Tessellate S.T.E.M.S (2019)  Mathematics  Category B  Set 3
 Tessellate S.T.E.M.S (2019)  Mathematics  Category C  Set 3
Computer Science
Sample Papers:
 Tessellate S.T.E.M.S (2019)  Computer Science  School  Sample Paper
 Tessellate S.T.E.M.S (2019)  Computer Science  College  Sample Paper
Practice Sets:
 Tessellate S.T.E.M.S (2019)  Computer Science  School  Set 1
 Tessellate S.T.E.M.S (2019)  Computer Science  School  Set 2
 Tessellate S.T.E.M.S (2019)  Computer Science  School  Set 3
 Tessellate S.T.E.M.S (2019)  Computer Science  College  Set 1
 Tessellate S.T.E.M.S (2019)  Computer Science  College  Set 2
 Tessellate S.T.E.M.S (2019)  Computer Science  College  Set 3
Physics
Sample Papers:
 Tessellate S.T.E.M.S (2019)  Physics  Category A  Sample Paper
 Tessellate S.T.E.M.S (2019)  Physics  Category B  Sample Paper
 Tessellate S.T.E.M.S (2019)  Physics  Category C  Sample Paper
Practice Sets:
Video Lectures for Preparation
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.
Syllabus: Mathematics
Section A
Combinatorics
 Basic Counting (Rule of Sum, Rule of Product, Combinations, Permutations, Principle of InclusionExclusion)
 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 (AMGM, CauchySchwartz, Rearrangement, Schur's Inequality)
 Exponents, Logarithms and Trigonometric Functions
 Complex Numbers (DeMoivre, 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

 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
Syllabus: Physics
Section A
 Mechanics
 Distance and Displacement
 Velocity
 Uniform and Nonuniform Motion along a Straight Line
 Acceleration
 Distancetime and Velocitytime 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  Righthand 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
 BiotSavart'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, Halflife and Mean Life, Binding Energy and its Calculation, Fission and Fusion Processes
 Photoelectric Effect
 Bohr's Theory of Hydrogenlike 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
 XRays
 Atoms in Electric and Magnetic Fields
Syllabus: Computer Science
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.)
 Numbertheoretic 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, Pspace etc.)
 Reductions and completeness
 Interactive proofs, probabilistically checkable proofs
 Hardness of approximation
Theory of Computation:
 DFA/NFA and regular languages
 Contextfree grammars and pushdown automata
 Turing machines / Oracle Turing machines
Discrete Mathematics:
 Graph theory
 Enumerative combinatorics
 Probability
Logic:
 Propositional logic
 Firstorder 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.
Previous Editions
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.