Welcome To B. K. Birla College of Arts, Science & Commerce, Kalyan
Welcome To B. K. Birla College of Arts, Science & Commerce, Kalyan
Welcome To B. K. Birla College of Arts, Science & Commerce, Kalyan
Welcome To B. K. Birla College of Arts, Science & Commerce, Kalyan
Welcome To B. K. Birla College of Arts, Science & Commerce, Kalyan
B. Sc. Mathematics
B. Sc. Mathematics
Key Information
Eligibility
- Student should have passed Standard XII Examination conducted by the Maharashtra State Board of Secondary and Higher Secondary education, Mumbai or an examination recognised as equivalent with subjects as may be specified by the University in Arts, Science and Commerce.
Duration
3 Years
Programme Code
Course Type
Bachelor Degree
Curriculum
Semester - I
Course Outcomes (CO)
| Title of Course | Course Outcome |
|---|---|
| Calculus-I and Algebra-I |
After completing students will be able to 1. understand order properties of real numbers. 2. understand concepts of intervals and neighbourhood. 3. understand types of sequences of real numbers and to find its limit. 4. memorise basic concepts of integers like divisibility, gcd, lcm, prime numbers, fundamental theorem of arithmetic. 5. Describe the properties of congruence and their applications, Fermat’s theorem, Euler’s theorem, Wilson’s theorem. 6. Differentiate the reducible and irreducible polynomials. 7. Construct the polynomials for given roots. |
| Applied Mathematics-I |
After completing students will be able to 1. Interpret data and plot Column Graphs, Bar Graphs, Line Charts, Pie Chart, Venn Diagrams 2. Differentiate between Relations and Functions 3. Learn about sets and Matrices. |
Semester - II
Course Outcomes (CO)
| Title of Course | Course Outcome |
|---|---|
| Calculus-II and Linear Algebra-I |
After completing students will be able to 1. understand the concept of limit and continuity. 2. use the algebra and properties of continuous functions. 3. understand the concept of differentiability. 4. find derivatives and understand the applications. 5. experiment with the system of linear equation and matrices. 6. To solve system of linear equation using Gaussian elimination method. 7. List the all axioms of vector spaces. 8. Identify the given set is a vector space. |
| Applied Mathematics-II |
After completing students will be able to 1. Interpret data and plot Column Graphs, Bar Graphs, Line Charts, Pie Chart, Venn Diagrams 2. Differentiate between Relations and Functions 3. Learn about sets and Matrices |
Semester - III
Course Outcomes (CO)
| Title of Course | Course Outcome |
|---|---|
| Calculus-III |
After completing students will be able to 1. Identify Riemann Integrable functions. 2. Analyse applications of integration. 3. Apply definite integral. 4. Examine the convergence of improper integrals. 5. Solve Ordinary Differential Equations |
| Linear Algebra-II |
After completing students will be able to 1. understand the basic concepts of vectors, matrices, and systems of linear equations. 2. learn about vector spaces, subspaces, basis, and dimension. 3. explore linear transformations and their properties. 4. understand concept of determinants. 5. study properties of inner products. |
| Discrete Mathematics |
After completing students will be able to 1. Identify countable and uncountable sets. 2. Apply two way counting. 3. Apply Pigeon – hole principle. 4. Apply the theory of permutations. 5. Solve recurrence relations. |
| Set Theory and Logic |
After completing students will be able to 1. understand the basic concepts of set theory 2. explore different types of sets and their properties (finite, infinite, empty, etc.). 3. understand logical connectives (AND, OR, NOT, IMPLIES, IF AND ONLY IF). |
| Computing with Python |
After completing students will be able to 1. understand the basics of Python programming language, including syntax, data types, and variables. 2. write Python code to perform arithmetic operations, manipulate strings, and work with data structures such as lists and dictionaries. |
Semester - IV
Course Outcomes (CO)
| Title of Course | Course Outcome |
|---|---|
| Calculus-IV |
After completing students will be able 1. To compare properties of functions of several variables with those of functions of one variable. 2. To calculate directional derivatives and partial derivatives of scalar fields. 3. To differentiate scalar and vector field. 4. To examine the continuity of scalar field. 5. To investigate maxima and minima of a function of two variables. |
| Linear Algebra-III |
After completing students will be able to 1. learn quotient spaces and orthogonal transformations 2. calculate eigenvalues and eigenvectors 3. analyze diagonalization |
| Ordinary Differential Equations |
After completing students will be able 1. To classify first order ODE as homogenous and non-homogenous ODE. 2. To solve first order first degree ODE and higher order LDE. 3. To model simple physics problems as ODE. 4. To examine existence of solution of first order first degree ODE. 5. To find orthogonal trajectories. |
| Commercial Mathematics |
After completing students will be able to 1. learn concepts of Relations and functions 2. learn concept of permutation and combination with application problems. 3. learn concept of probability, definitions of events, occurrences of events. 4. learn some rules of probability and application problems 5. learn to calculate percentage and ratios in application problems. 6. learn definitions of proportions and properties. |
| Applied Linear Algebra using Python |
After completing students will be able to 1. Understand the fundamental concepts of linear algebra and their applications. 2. Develop proficiency in using Python libraries such as NumPy and SciPy for linear algebra computations. 3. Apply linear algebra techniques to solve problems in various domains, including data science and machine learning. |
Semester - V
Course Outcomes (CO)
| Title of Course | Course Outcome |
|---|---|
| Algebra-II |
After completing students will be able to 1. Understand the definition, properties, and structures of groups and subgroups. 2. Analyze and solve mathematical problems using symmetry and group properties. 3. Apply group-theoretic concepts such as homomorphism’s, isomorphism’s, etc. |
| Topology of Metric Spaces |
After completing students will be able to 1. Understand the fundamental concepts and properties of metric spaces and normed linear spaces. 2. Analyze sequences in metric spaces, including their convergence and relationships to completeness. 3. Apply key theorems like the Nested Interval Theorem and Heine-Borel Property to solve problems in topology. |
| Laplace Transforms and Applications |
After completing students will be able to 1. Know the use of Laplace transform in system modeling, digital signal processing, process control. 2. Solve an initial value problem for an nth order ordinary differential equation using the Laplace transform. |
| Integral Calculus |
After completing students will be able to 1. Define and explain the concept of multiple integration. 2. Use integration techniques in real-world problems, such as calculating the moment of inertia, work done by a force, and electric fields. 3. Understand the physical, geometric, and algebraic significance of integrals, such as finding areas, volumes, and accumulated quantities. 4. Solve problems involving the center of mass, work done using integration. 5. Apply Green, Divergence and Stokes theorem. |
| Introduction to Sage Math |
After completing students will be able to 1. Understand the basics of Sage Math and its interface. 2. Apply Sage Math to solve problems in algebra, calculus, linear algebra, and other mathematical domains. |
Semester - VI
Course Outcomes (CO)
| Title of Course | Course Outcome |
|---|---|
| Algebra-III |
After completing students will be able to 1. Understand the definitions and properties of rings, subrings, ideals, and ring homomorphism’s. 2. Analyze and work with rings, such as commutative rings, integral domains, and fields. 3. Explore the structure and properties of polynomial rings and factorization in rings. |
| Topology of Metric Spaces and Real Analysis |
After completing students will be able to 1. Understand the concepts of continuity, uniform continuity, and connectedness in metric spaces. 2. Analyze the convergence of Fourier series and sequences of functions, including uniform convergence and its implications. 3. Apply the properties of power series and their convergence to study functions like exponential, sine, and cosine. |
| Fourier Transforms and Fourier Series |
After completing students will be able to 1. understand the concept of Fourier transforms and their corresponding inversion techniques. 2. understand the various applications of Fourier transforms. |
| Complex Analysis |
After completing students will be able to 1. Identify analytic functions. 2. Apply Cauchy Integral Formula. 3. Apply Taylors Theorem. 4. Find Laurent’s expansions. 5. Solve Contour Integrals. |
Expert Faculty
Mr. Prakash Sansare
HOD - Mathematics
Assistant Professor
Assistant Professor
Maths
Mr. Gajanan Dhumal
Assistant Professor
Maths
Dr. Krishna Ghode
Assistant Professor
Maths
Mrs. Pradnya Chande
Assistant Professor (Ad-hoc)
Maths
Ms. Komal Badgujar
Assistant Professor (CHB)
Maths
Mrs. Vaibhavi Mulmule
Assistant Professor(CHB)
Maths
Ms. Rupali Dudhamal
Assistant Professor(CHB)
Maths
Program Outcome (PO)
PO-1 : Fundamental Acquisition
Acquire the fundamentals of the course.
PO-2 : Scientific Temper
Scientific temper will be developed in Students.
PO-3 : Practical Skills
Students will acquire basic Practical skills & Technical knowledge along with domain knowledge of different subjects in the science stream.
PO-4 : Employability
Students will become employable; they will be eligible for career opportunities in Industry or will be able to opt for entrepreneurship.
PO-5 : Subject Knowledge
Students will possess basic subject knowledge required for higher studies, professional and applied courses like Management Studies, Law etc.
PO-6 : Analytical Aptitude
Develop an analytical aptitude.
PO-7 : Holistic Development
Aids all-round development of students.
PO-8 : Environmental Awareness
Sensitize towards environment and sustainability.
PO-9 : Lifelong Learning
Orient students towards lifelong learning.
Programme Specific Outcomes (PSO)
PSO1 : Logical Reasoning
Formulate and develop mathematical arguments in a logical manner.
PSO2 : Quantitative Modeling
Understand, formulate and use quantitative models arising in social science, business and other contexts.
PSO3 : Mathematical Reasoning
Inculcate mathematical reasoning.
PSO4 : Problem Solving
Nurture problem solving skills, thinking, creativity through assignments, project work.
PSO5 : Program Design
Design program in Python and Scilab applications.
Programme Objectives
- Loreum Ipsum
Career Options
- Loreum Ipsum
