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    CMI BS Hons 2026: Exam Preparation, Syllabus, Tests & Notes

    CMI’s four-year B.S. (Honours) programmes in Mathematics, Mathematics and Computer Science.

    CMI BS Hons Study Notes & Chapter List 2026

    Probability Chapter Study Notes

    Random variables

    Elementary Probability

    Conditional Probability

    Logic, Proof and Mathematical Thinking Chapter Study Notes

    Statements and Quantifiers

    Problem-solving reasoning

    Proof Methods

    Vectors, Matrices and 3D Geometry Chapter Study Notes

    Matrices and Determinants

    3D Geometry

    Vectors

    Calculus Chapter Study Notes

    Calculus - Unit 1

    Unit 1 — Calculus

    Unit 2 — Calculus

    Calculus-based reasoning

    Integral Calculus

    Differentiation

    Limits and Continuity

    Combinatorics and Discrete Mathematics Chapter Study Notes

    Basic Counting

    Discrete structures and strategy

    Paths and Recurrences

    Advanced Counting

    Algebra and Functions Chapter Study Notes

    Polynomials and Equations

    Algebraic Expressions

    Relations and Functions

    Sequences and Series

    Number Theory Chapter Study Notes

    Divisibility and Factorisation

    Modular Arithmetic

    Number-theoretic reasoning

    Integer Equations

    Trigonometry and Complex Numbers Chapter Study Notes

    Trigonometry

    Complex Numbers

    Geometry Chapter Study Notes

    Transformational and Locus Geometry

    Euclidean Geometry

    Coordinate Geometry

    Inequalities and Estimation Chapter Study Notes

    Algebraic inequalities

    Functional and sequence inequalities

    CMI BS Hons Short Notes & Revision Summaries 2026

    Probability Short Notes & Revision

    Random variables

    Elementary Probability

    Conditional Probability

    Logic, Proof and Mathematical Thinking Short Notes & Revision

    Statements and Quantifiers

    Problem-solving reasoning

    Proof Methods

    Vectors, Matrices and 3D Geometry Short Notes & Revision

    Matrices and Determinants

    3D Geometry

    Vectors

    Calculus Short Notes & Revision

    Calculus - Unit 1

    Unit 1 — Calculus

    Unit 2 — Calculus

    Calculus-based reasoning

    Integral Calculus

    Differentiation

    Limits and Continuity

    Combinatorics and Discrete Mathematics Short Notes & Revision

    Basic Counting

    Discrete structures and strategy

    Paths and Recurrences

    Advanced Counting

    Algebra and Functions Short Notes & Revision

    Polynomials and Equations

    Algebraic Expressions

    Relations and Functions

    Sequences and Series

    Number Theory Short Notes & Revision

    Divisibility and Factorisation

    Modular Arithmetic

    Number-theoretic reasoning

    Integer Equations

    Trigonometry and Complex Numbers Short Notes & Revision

    Trigonometry

    Complex Numbers

    Geometry Short Notes & Revision

    Transformational and Locus Geometry

    Euclidean Geometry

    Coordinate Geometry

    Inequalities and Estimation Short Notes & Revision

    Algebraic inequalities

    Functional and sequence inequalities

    CMI BS Hons Chapter-wise Practice Questions 2026

    Probability Practice Questions

    Random variables

    Elementary Probability

    Conditional Probability

    Logic, Proof and Mathematical Thinking Practice Questions

    Statements and Quantifiers

    Problem-solving reasoning

    Proof Methods

    Vectors, Matrices and 3D Geometry Practice Questions

    Matrices and Determinants

    3D Geometry

    Vectors

    Calculus Practice Questions

    Calculus - Unit 1

    Unit 1 — Calculus

    Unit 2 — Calculus

    Calculus-based reasoning

    Integral Calculus

    Differentiation

    Limits and Continuity

    Combinatorics and Discrete Mathematics Practice Questions

    Basic Counting

    Discrete structures and strategy

    Paths and Recurrences

    Advanced Counting

    Algebra and Functions Practice Questions

    Polynomials and Equations

    Algebraic Expressions

    Relations and Functions

    Sequences and Series

    Number Theory Practice Questions

    Divisibility and Factorisation

    Modular Arithmetic

    Number-theoretic reasoning

    Integer Equations

    Trigonometry and Complex Numbers Practice Questions

    Trigonometry

    Complex Numbers

    Geometry Practice Questions

    Transformational and Locus Geometry

    Euclidean Geometry

    Coordinate Geometry

    Inequalities and Estimation Practice Questions

    Algebraic inequalities

    Functional and sequence inequalities

    CMI BS Hons Chapter-wise Previous Year Questions (PYQs) 2026

    Probability Past Year Questions

    Random variables

    Elementary Probability

    Conditional Probability

    Logic, Proof and Mathematical Thinking Past Year Questions

    Statements and Quantifiers

    Problem-solving reasoning

    Proof Methods

    Vectors, Matrices and 3D Geometry Past Year Questions

    Matrices and Determinants

    3D Geometry

    Vectors

    Calculus Past Year Questions

    Calculus - Unit 1

    Unit 1 — Calculus

    Unit 2 — Calculus

    Calculus-based reasoning

    Integral Calculus

    Differentiation

    Limits and Continuity

    Combinatorics and Discrete Mathematics Past Year Questions

    Basic Counting

    Discrete structures and strategy

    Paths and Recurrences

    Advanced Counting

    Algebra and Functions Past Year Questions

    Polynomials and Equations

    Algebraic Expressions

    Relations and Functions

    Sequences and Series

    Number Theory Past Year Questions

    Divisibility and Factorisation

    Modular Arithmetic

    Number-theoretic reasoning

    Integer Equations

    Trigonometry and Complex Numbers Past Year Questions

    Trigonometry

    Complex Numbers

    Geometry Past Year Questions

    Transformational and Locus Geometry

    Euclidean Geometry

    Coordinate Geometry

    Inequalities and Estimation Past Year Questions

    Algebraic inequalities

    Functional and sequence inequalities

    Description

    CMI’s four-year B.S. (Honours) programmes in Mathematics, Mathematics and Computer Science.

    Placement Statistics

    Placement Snapshot

    Metric2025 cycle
    Highest CTC₹ 47 LPA
    Average CTC₹ 18 LPA
    Median CTC₹ 17 LPA
    Placement ratio~ 80 % (rest choose MS/PhD abroad)
    Top recruitersGoogle, Jane Street, Adobe, Tower Research, Morgan Stanley

    Course Overview

    CMI BS (Hons) - Entrance Guide 2026

    A four-year honours programme that fuses deep mathematics with modern computer science.

    This page answers the big five questions students ask:

    1. What is the CMI entrance exam?

    2. Who can apply and what are the exact eligibility rules?

    3. What is the paper pattern and marking scheme?

    4. What topics appear in the syllabus?

    5. How do I prepare effectively in 12 weeks?

    The information below reflects the official schedule published for the August 2026 intake.

    Entrance Exam Details

    2026 Application Calendar

    MilestoneDate
    Online form opens2 Mar 2026
    Form & fee deadline4 Apr 2026 - 23:59 IST
    Admit card download25 Apr 2026
    Exam day2 May 2026 (14 : 00 - 17 : 00)
    Results≈ early June 2026

    Test centres (34 total)

    Agartala, Ahmedabad, Allahabad, Bangalore, Bhubaneswar, Calicut, Chennai, Cochin, Coimbatore, Durgapur, Goa, Gurgaon, Guwahati, Hyderabad, Imphal, Indore, Jaipur, Kanpur, Kolkata, Madurai, Mohali, Mumbai, Nagpur, New Delhi, Noida, Paschim Medinipur, Patna, Pune, Raipur, Ranchi, Shillong, Silchar, Siliguri, Srinagar, Tiruchi, Trivandrum, Visakhapatnam. :contentReference[oaicite:0]{index=0}

    Exam Pattern

    PartSection typeQuestionsMarksNegativeNotes
    AMCQ (single-correct)1040-1 per wrongMinimum 24 / 40 needed for Part B to be evaluated
    BSix long-answer proofs6600Step-wise marking for rigour
    Total161003-hour pen-and-paper test

    *Paper date*: 2 May 2026 (14:00 - 17:00 IST) :contentReference[oaicite:0]{index=0}.

    Pattern remains unchanged from the 2025 cycle :contentReference[oaicite:1]{index=1}.

    Skills Learning Outcomes

    • Write rigorous proofs and communicate findings clearly.
    • Analyse algorithmic complexity and optimise code.
    • Model data sets and run statistical inference.
    • Build production-ready programs in Python/C++ with *Git* workflows.
    • Collaborate on research projects and defend results in seminars.

    Admission Procedure

    1. Register online at apply2026.cmi.ac.in (₹ 1 000).

    2. Fill personal + Class 12 details; upload photo/signature.

    3. Pay fee → receive confirmation e-mail.

    4. Download admit card from 25 Apr 2026.

    5. Write exam on 2 May 2026 at chosen centre.

    6. If selected (cut-off met), complete on-campus counselling and pay first-semester fee within 7 days. :contentReference[oaicite:1]{index=1}

    Preparation Strategy

    PhaseWeeksFocusDeliverable
    Concept Build1 - 4Finish theory; make flash cardsAll core formulas memorised
    Drill5 - 8Daily 30 MCQ + 1 proofError log & weekly recap
    Mock Loop9 - 11Six full papers under 3-h timerAnalytics + topic-wise fix
    Taper12Light revision, sleep hygiene, exam-day kitReady checklist

    Tip: aim for ≥ 24/40 in Part A by week 8-the gate to having Part B evaluated.

    Syllabus

    Unit-wise list

    UnitKey topics
    Logic & ProofsStatements, induction, contradiction
    Algebra & Number TheoryModular arithmetic, binomial theorem, inequalities
    Geometry & TrigonometryEuclidean geometry, coordinate geometry, trig identities
    CalculusLimits, continuity, derivatives, integrals, sequences & series
    CombinatoricsPermutations, combinations, Pigeonhole principle, basic graph ideas
    ProbabilityRandom variables, expectation, basic distributions

    Notes

    Complete lecture notes (250 pages) covering all six units, each with:

    1. Concept exposition

    2. Worked examples

    3. “Checkpoint” quizzes

    4. Proof templates

    5. End-of-unit mixed drill

    Short Notes

    Cheat-sheets for last-week revision: formula tables, derivative ladders, binomial identities, common proof tricks, algorithm pseudocode snippets.

    Chapter Wise Questions

    430 previous-year questions sorted into 42 chapters + 820 fresh practice problems (difficulty graded Easy → Advanced).

    Full Length Mocks

    15 timed mocks that mimic the latest pattern (MCQ gate → long proofs) with instant analytics and percentile ranking.

    Course Curriculum

    Eight-Semester Plan

    SemCore PapersLab / SeminarOpen ElectiveMilestone
    ICalculus I · Discrete MathsIntro Python-Quiz-1
    IILinear Algebra · ProbabilityDS & Algo Lab-Hackathon
    IIICalculus II · AlgorithmsC++ Lab-Mini-proj
    IVAbstract Algebra · StatisticsR Lab1Mini-thesis
    VReal Analysis · CombinatoricsML Basics1Term Paper
    VIGraph Theory · Number TheoryAdvanced Python1Internship
    VIINumerical Methods · TopologyResearch Seminar2Thesis - Part 1
    VIIIElectives (2)Thesis Workshop2Thesis - Defence

    Day In Life

    TimeActivity
    07 : 30Breakfast & daily puzzle
    09 - 13Lectures / tutorials
    14 - 16Lab / library research
    16 : 15Tea break & Ultimate Frisbee
    18 : 00Club meets / seminar talk
    21 : 00Self-study or gaming jam

    Campus Life

    Life at CMI

    • Housing : Single rooms with 1 Gbps Wi-Fi; common lounges on every floor.
    • Library : 24 × 7 access, 25 k+ titles, MathSciNet & JSTOR subscriptions.
    • Food : Veg + non-veg mess, evening snack bar, late-night Maggi kiosk.
    • Clubs : π-Club (puzzles), Coding-Nights, Carnatic-Music, Anime-Circle, Football.
    • Events : “Infinity” math fest in September; ICPC regional coding prelims in December.

    Alumni Stories

    > Rajiv ’19 → Quant Analyst, Jane Street

    > “Proof drills in Part B prepared me for brain-teaser interviews.”

    > Sneha ’20 → PhD, MIT EECS

    > “The research seminar in Sem VII gave me my first paper and a strong letter.”

    Global Exposure

    • 10 % of each batch secures funded *summer research* at EPFL, ENS-Paris, or Waterloo.
    • Exchange MoUs with Uni of Bonn and NTU Singapore (one-semester swap, credit transfer).
    • ACM-ICPC regionals participation every year since 2013.

    Course Comparison

    FeatureCMI BS (Hons)ISI BMathIISc BSc (Research)
    Intake6050120
    Fees / yr₹ 1.2 L₹ 20 k₹ 2 L
    Core focusMaths + CSPure MathsInter-disciplinary STEM
    Entrance difficultyHighVery HighModerate
    Avg CTC₹ 18 LPA₹ 12 LPA₹ 24 LPA
    Research thesisMandatory (Sem VIII)OptionalOptional

    Eligibility Criteria

    • Passed (or appearing for) Class 12 or equivalent in 2024 / 2025 / 2026.
    • Open to all streams, but strong background in Mathematics expected.
    • No age limit.
    • *Direct admission*: students who qualified for IMO/IOI/other listed National Olympiad camps may be exempted from the entrance exam​-​decided by the Admissions Committee.

    Placement

    Graduates land roles in quantitative finance, software engineering, data science and research-oriented positions. About 20 % of the class proceeds directly to funded MS/PhD programmes at institutes such as MIT, ETH Zürich, CMU and IISc. On-campus recruitment typically happens in January, with resume workshops and mock interviews run by the alumni network.

    Course Outcome

    Graduates exit with deep mathematical rigour plus practical coding skill, ready for top MS/PhD programmes or high-impact tech roles.

    Course Outcomes

    1. Abstract reasoning & problem formalisation

    2. Algorithmic thinking & software engineering discipline

    3. Quantitative data analysis competency

    4. Scientific communication-LaTeX papers & oral defence

    5. Independent research capability

    Industry Applications

    • Quantitative trading & finance
    • Machine learning & data analytics
    • Cryptography & cyber-security
    • Optimisation & operations research
    • Scientific computing & simulation

    Tools And Technologies

    Python · C++ · R · MATLAB · Git · LaTeX · Linux

    Learning Pathway

    Concept → Practice → Mock → Review → Revise

    > Master each unit, drill with chapter-wise sets, sit full mocks, analyse gaps, then do targeted revision.

    Syllabus Key Takeaway

    Proof-centric exam: Calculus + Linear Algebra dominate Part A; discrete-maths proofs headline Part B. Master fundamentals, then practise timed proofs for speed & clarity.

    Unit Test Keys

    Logic,Algebra,Geometry,Calculus,Combinatorics,Probability

    Question Pattern Analysis

    PartMarksTypical topic mix (last 3 yrs)
    A (40 marks)MCQ + NATCalculus 40 % · Linear Algebra 30 % · NT/Combinatorics 30 %
    B (60 marks)Long proofsProof-based problems drawn roughly 1 each from calculus, combinatorics, number theory, geometry, algebra, inequalities

    Key rule: Part B is *checked only if you score ≥ 24 / 40 in Part A*. :contentReference[oaicite:3]{index=3}

    Placement Analysis

    Year-on-Year CTC Trend

    YearHighest (₹ L)Average (₹ L)Median (₹ L)
    2025471817
    2024621816
    2023201615

    *Insight*: Highest offers fluctuate with quant-firm intake, but average has held between ₹ 16-18 LPA for three years, signalling stable market demand.

    Cutoff Analysis

    Historical Cut-offs (out of 120 marks)

    YearPart A screen (40)Overall cut-off - *No scholarship*Overall cut-off - *With scholarship*
    20251647 (Gen) · 44 (Others)59 (Gen) · 49 (Others)
    20241147 (Gen) · 39 (Others)58 (Gen) · 47 (Others)
    2023836 (Gen M) · 33 (Others)-

    *Sources*: cmientranceexam.in cut-off archive :contentReference[oaicite:0]{index=0} and student-shared data matched by MathDigiLab :contentReference[oaicite:1]{index=1}.

    #### What this means for 2026

    • The overall cut-off hovers around 40 % of the paper.
    • The 2026 paper has been reduced to 100 marks (40 MCQ + 60 proof). Scaling the trend → expect ≈ 40/100 for a general-category offer.
    • Part A gate is likely to remain at ~ 10-12 / 40.

    We will update this table on result day for real numbers.

    Test Instructions

    Exam-day checklist

    • Reach centre by 13 : 15 IST with printed admit card & photo ID
    • Allowed stationery: HB pencil, blue/black pen, eraser-no calculators
    • Part A: darken bubbles fully; rough work in margins
    • Part B: start each proof on a fresh page; box final answers
    • Transparent water bottle permitted; follow 2026 safety advisory

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    CMI BS Hons Preparation Resources 2026