## B.Sc.(H) Mathematics Course ,Syllabus, & Eligibility

2 years ago

Life is a theory, you just need motivation, persistence, consistency to prove it in order to make it an Axiom.

Among the numerous choices available to us in this era, one of the most compatible options for a science geek is Mathematics honors. .Every student after class 12 faces a dilemma which is quite natural in this world. But if you are a logic lover, analytic master, calculation enthrall then Mathematics is a coveted choice for you. If the geometry shapes of circle, hyperbola, parabola, ellipse fascinate you then **CONGO ! **you are made for this course.

**How to identify your tilt towards the subject?**

It is said that”, If you love doing something then you would spend hours doing that”. So just start with a pencil and paper, start solving your syllabus questions identify whether it’s similar to your hobby.

**Is the working experience riveting for you?**

If the answer is yes then no need to perturb just have the choice of Mathematics Hons.

Not every person needs to be Einstein in order to solve equations. So in order to make your coefficient of life unique, just work diligently. And once the journey of college life starts then life comes up with many blatant experiences.

**What do you need to keep in mind while choosing the B.Sc (H) Maths course?**

**Sincerity, hard work, and punctuality are the keys to attain success in any field particularly in maths and science****Just have focus and faith while pursuing the course. Have confidence in your solutions.****Don’t procrastinate work for the next day.****Maintain a diary of assignments, projects, test series.**

__Eligibility Criteria of the B.Sc Maths (Hons) course__

For any student to be eligible, should fulfil the following criteria’s:

**The student should have maths as one of the subjects in 10+2.****There is no such age-eligible criteria.****In this era of throat-cutting competition different universities have different cut-offs. So one must score decent marks so as to get in a dream college.**

These are some eligibility for the above-mentioned course and they may vary from college to college.

Let’s have a glance at the syllabus of this course so that we could manifest a clear picture. Don’t be at the circumference of the circle be at the center so that everything is in your reach equally.

__SYLLABUS of B.Sc Mathematics (Hons)__

**IN THIS COURSE THERE ARE SIX SEMESTERS EACH SEMESTER HAS 2 OR 3 CORE SUBJECTS AND 1 OPTIONAL SUBJECT. AND IN 5 AND 6 SEMESTER THERE ARE NO OPTIONAL SUBJECT (GENERAL ELECTIVE).**

__SEMESTER 1__

**C1- Calculus**

Hyperbolic functions, Higher order derivatives, Applications of Leibnitz rule. The first derivative test, concavity and inflection points, Second derivative test, Curve sketching using Parametric representation of curves and tracing of parametric curves

**C2- Algebra**

Polar representation of complex numbers, nth roots of unity, De Moiré’s theorem for rational indices and its applications. [Equivalence relations, Functions, Composition of functions, Invertible functions.

__SEMESTER 2__

**C3-RealANALYSIS**

**R**. Bounded above sets, Bounded below sets, Bounded Sets, Unbounded sets, Suprema and Infima, The Completeness Property of R, The Archimedean Property, Density of Rational (and Irrational) numbers in R, Intervals. Limit points of a set, Isolated points, Illustrations of Bolzano-Weierstrass theorem for sets.

**C4- Differential Equations**

Differential equations and mathematical models, order and degree of a differential equation, exact differential equations and integrating factors of first order differential equations, reducible second order differential equations, application of first order differential equations to acceleration-velocity model, growth and decay model. Introduction to compartmental models .

__SEMESTER 3__

**C5 Theory of Real Functions**

Limits of functions (epsilon-delta approach), sequential criterion for limits, divergence criteria. Limit theorems, one sided limits. Infinite limits & limits at infinity. Continuous functions, sequential criterion for continuity & discontinuity. & in an interval, Carathéodory’s theorem, algebra of differentiable functions.

**C6 Group Theory**

Symmetries of a square, Dihedral groups, definition and examples of groups including permutation groups and quaternion groups (illustration through matrices), elementary properties of groups. Subgroups and examples of subgroups, centralizer, normalizer, center of a group, product of two subgroups. Properties of cyclic groups.

**C7 Multivariate Calculus**

Functions of several variables, limit and continuity of functions of two variables. Partial differentiation, total differentiability and differentiability, sufficient condition for differentiability. Chain rule for one and two independent parameters, directional derivatives, the gradient, maximal and normal property of the gradient, tangent planes .

__SEMESTER 4__

1**C8 Partial Differential Equations**

Introduction, classification, construction and geometrical interpretation of first order partial differential equations (PDE), method of characteristic and general solution of first order PDE, canonical form of first order PDE, method of separation of variables for first order PDE.

**C9 Riemann Integration & Series of Function**

Riemann integration; inequalities of upper and lower sums; Riemann conditions of integrability. Riemann sum and definition of Riemann integral through Riemann sums; equivalence of two definitions; Riemann integrability of monotone and continuous functions, Properties of the Riemann integral; definition and integrability of piecewise continuous and monotone functions. Intermediate Value theorem for Integral

**C 10 Ring Theory & Linear Algebra-I**

Definition and examples of rings, properties of rings, subrings, integral domains and fields, characteristic of a ring. Ideals, ideal generated by a subset of a ring, factor rings, operations on ideals, prime and maximal ideals.

__SEMESTER 5__

**C 11 Metric Spaces**

Metric spaces: definition and examples. Sequences in metric spaces, Cauchy sequences. Complete Metric Spaces. Open and closed balls, neighbourhood, open set, interior of a set, Limit point of a set, closed set, diameter of a set, Cantor’s Theorem, Subspaces, dense sets, separable spaces. [1] Continuous mappings, sequential criterion and other characterizations of continuity, Uniform continuity.

**C 12 Group Theory-II**

Automorphism, inner automorphism, automorphism groups, automorphism groups of finite and infinite cyclic groups, applications of factor groups to automorphism groups, Characteristic subgroups, Commutator subgroup and its properties.

__SEMESTER 6__

**C13 Complex Analysis**

Limits, Limits involving the point at infinity, continuity. Properties of complex numbers, regions in the complex plane, functions of complex variable, mappings. Derivatives, differentiation formulas, Cauchy-Riemann equations, sufficient conditions for differentiability.

**C 14 Ring Theory and Linear Algebra – II**

Polynomial rings over commutative rings, division algorithm and consequences, principal ideal domains, factorization of polynomials, reducibility tests, irreducibility tests, Eisenstein criterion, unique factorization in Z[x]. Divisibility in integral domains, irreducibles, primes, unique factorization domains, Euclidean domains.

For the whole syllabus you can visit any university website too.

**What we need to keep in mind in a world of a strenuous horse race is that follow your interest and passion.**

**BE YOU….DON’T be an ape.**

Your choices and your success will define your life .