B. K. BIRLA COLLEGE OF ARTS, SCIENCE AND COMMERCE .
B. K. BIRLA COLLEGE OF ARTS, SCIENCE AND COMMERCE(AUTONOMOUS)KALYAN (W)Affiliated to University of MumbaiDEPARTMENT OF MATHEMATICSProgramme: Bachelor of Science (B.Sc.)SYLLABUS FOR:Science Faculty: F. Y. B. Sc., S. Y. B. Sc., T. Y. B. Sc.Commerce Faculty: F. Y. B. Com., T. Y. B. Com.Community College : Certificate course, Advance Certificate Course,Diploma in Accounting and TaxationCertificate Course:1. Basic and advance Excel and LaTeX.2. SciLab
Choice Based Credit System (CBCS) with effect from the academicyear 2018-19B. K. BIRLA COLLEGE OF ARTS, SCIENCE AND COMMERCE(AUTONOMOUS)KALYAN (W)Affiliated to University of MumbaiChoice Based Credit System (CBCS) with effect from the academicyear 2018-19Faculty of ScienceGuidelinesSyllabus Structure:1. In F.Y.B.Sc. (CBCS) in Semester I and II, there will be two papers each with 2credits and one practical of 2 credits in each semester2. In S.Y.B.Sc (CBCS) in Semester III and Semester IV, there will be three paperswith 2 credits each in both the semesters and one practical of 3 credits in eachsemester.3. In T.Y.B.Sc. (CBCS) in Sem V and VI, there will be three compulsory paper eachwith 2.5 credits in each semester, one elective paper and one applied componentwith 2.5 credits each in each semester and three practicals of 3 credits each in eachsemester.Evaluation:1. In F.Y.B.Sc. (CBCS) in Sem I and II the Core Course will be theory and practical.The College will conduct all the semester examinations of 100 marks per CoreCourse in the prescribed pattern of 40 marks of internal assessment and 60 marksfor semester end examination. The student will have to secure a minimum of 40%marks in internal assessment as well as semester end examination. The collegewill conduct a practical examination of 50 marks for each paper.
2. In each semester, the student will have to submit Project/ Assignment/Journal forCore Courses in the College before appearing for the Semester End Examination.The last date of submission of the Project will be officially declared by theCollege.3. The Project work will be carried out by the student with the guidance of theconcerned faculty member who will be allotted to the student as the Guide for theProject.4. In each semester, for Core Courses the student will have to secure a minimum of40% marks in aggregate and a minimum of 40% in each component of assessmenti.e. 16 out of 40 marks in Internal Evaluation and 24 out of 60 marks in semesterend examination/ Practical Examination.5. In S.Y.B.Sc. (CBCS) in Sem III and IV the Core Course will be theory andpractical. The College will conduct all the semester examinations of 100 marks perCore Course in the prescribed pattern of 40 marks of internal assessment and 60marks for semester end examination. The student will have to secure a minimumof 40% marks in internal assessment as well as semester end examination. Thecollege will conduct a practical examination of 50 marks for each paper.6. In each semester, the student will have to submit Project/ Assignment/Journal forCore Courses in the College before appearing for the Semester End Examination.The last date of submission of the Project will be officially declared by theCollege.7. The Project work will be carried out by the student with the guidance of theconcerned faculty member who will be allotted to the student as the Guide for theProject.8. In each semester, for Core Courses, the student will have to secure a minimum of40% marks in aggregate and a minimum of 40% in each component of assessmenti.e. 16 out of 40 marks in Internal Evaluation and 24 out of 60 marks in semesterend examination/ Practical Examination.
9. In T.Y.B.Sc. (CBCS) in Sem V and VI the Core Course and Elective Courses willbe theory and practical. The College will conduct all the semester examinations of100 marks per Core Course and Elective Courses in the prescribed pattern of 40marks of internal assessment and 60 marks for semester end examination. Thestudent will have to secure a minimum of 40% marks in internal assessment aswell as semester end examination. The college will conduct a practicalexamination of 50 marks for each core course and elective course and 100 marksfor applied component10. In each semester, the student will have to submit Project/ Assignment/Journal forCore Courses and Elective Courses in the College before appearing for theSemester End Examination. The last date of submission of the Project will beofficially declared by the College.11. The Project work will be carried out by the student with the guidance of theconcerned Faculty Member who will be allotted to the student as the Guide for theProject.12. In each semester, for Core Courses and Elective Courses, the student will have tosecure a minimum of 40% marks in aggregate and a minimum of 40% in eachcomponent of assessment i.e. 16 out of 40 marks in Internal Evaluation and 24 outof 60 marks in semester end examination/ Practical Examination.Note: All other rules regarding Standard of Passing, ATKT, etc., will be as perthose decided by the Faculty of Science passed by the Academic Council fromtime to time.
Faculty of CommerceGuidelinesSyllabus Structure:4. In F.Y.B.Com. (CBCS) in Sem I and II, there will be one compulsory paperMathematical and Statistical Techniques each with 3 credits in each semester.5. In T.Y.B.Com. (CBCS) in Sem V and Sem VI, there will be one Elective paperComputer System and Applications with 3 credits each in both the semesters.Evaluation:2. In F.Y.B.Com. (CBCS) in Sem I and II the Core Course Mathematical andStatistical Techniques will be theory. The College will conduct all the semesterexaminations of 100 marks per Core Course in the prescribed pattern of 40 marksof internal assessment and 60 marks for semester end examination. The studentwill have to secure a minimum of 40% marks in internal assessment as well assemester end examination.3. In T.Y.B.Com. (CBCS) in Sem V and Sem VI course, Computer System andApplications will be Electives. The College will conduct the semester examinationof 100 marks per course in the prescribed pattern of 40 marks of Internalassessment/Project Work and 60 marks for semester end examination/Practicalexamination. The student will have to secure a minimum of 40% marks in internalassessment as well as semester end examination per above Elective Course.13. In each semester, the student will have to submit Project/ Assignment/Journal forCore Courses and Elective Courses in the College before appearing for theSemester End Examination. The last date of submission of the Project will beofficially declared by the College.14. The Project work will be carried out by the student with the guidance of theconcerned Faculty Member who will be allotted to the student as the Guide for theProject.15. In each semester, for Core Courses and Elective Courses, the student will have tosecure a minimum of 40% marks in aggregate and a minimum of 40% in each
component of assessment i.e. 16 out of 40 marks in Internal Evaluation and 24 outof 60 marks in semester end examination/ Practical Examination.Note: All other rules regarding Standard of Passing, ATKT, etc., will be as perthose decided by the Faculty of Commerce passed by the Academic Council fromtime to time.
B. K. BIRLA COLLEGE OF ARTS, SCIENCE AND COMMERCE(AUTONOMOUS)KALYAN (W)Affiliated to University of MumbaiCONTENTProgramme- Bachelor of Science (B.Sc.)Sr. No.CourseCodeCredits1F.Y.B. Sc.– Calculus-IBUSMT101022F.Y.B. Sc. – Algebra-IBUSMT102023F.Y.B. Sc. – Practicals based on BUSMT101 &BUSMT102BUSMTP01024F.Y.B. Sc.– Calculus-IIBUSMT201025F.Y.B. Sc. – Linear Algebra-IBUSMT202026F.Y.B. Sc. –Practicals based on BUSMT201 & BUSMT202 BUSMTP02027S.Y. B. Sc. –Calculus-IIIBUSMT301028S.Y. B. Sc. – Linear Algebra-IIBUSMT302029S.Y. B. Sc. – Discrete MathematicsBUSMT3030210BUSMTP030311S.Y. B. Sc. – Practicals Based on BUSMT301, BUSMT302and BUSMT303S.Y. B. Sc. –Calculus-IVBUSMT4010212S.Y. B. Sc. – Linear Algebra-IIIBUSMT4020213S.Y. B. Sc. –Ordinary Differential EquationBUSMT4030214BUSMTP040315S.Y. B. Sc. – Practicals Based on BUSMT 401, BUSMT402 and BUSMT 403T.Y.B.Sc – Multivariable CalculusBUSMT5012.516T.Y.B.Sc – Algebra-IIBUSMT5022.517T.Y.B.Sc – Topology of Metric SpacesBUSMT5032.518T.Y.B.Sc – Numerical Analysis IBUSMT5A42.519T.Y.B.Sc –Number Theory and its Application IBUSMT5B42.5
20T.Y.B.Sc – Graph TheoryBUSMT5C42.521T.Y. B. Sc. – Practicals Based on BUSMT501,BUSMT502.BUSMTP05322T.Y. B. Sc. – Practicals Based on BUSMT503 andBUSMT5A4 OR BUSMT5B4 ORBUSMT5C4.BUSMTP06323T.Y.B.Sc – Basic Complex AnalysisBUSMT6012.524T.Y.B.Sc –BUSMT6022.525T.Y.B.Sc – Topology of Metric Spaces and Real AnalysisBUSMT6032.526T.Y.B.Sc – Numerical Analysis IIBUSMT6A42.527T.Y.B.Sc –Number Theory and its Application IIBUSMT6B42.528T.Y.B.Sc – Graph Theory and CombinatoricsBUSMT6C42.529T.Y. B. Sc. – Practicals Based on BUSMT601,BUSMT602.BUSMTP07330T.Y. B. Sc. – Practicals Based on BUSMT603 andBUSMT6A4 OR BUSMT6B4 ORBUSMT6C4.BUSMTP083Algebra-IIIProgramme – Bachelor of Commerce (B.Com.)Compulsory CourseSr. No.CourseCodeCredits1F.Y.B.Com. – Mathematical and Statistical Techniques -IBUBCOMFSI.6032F.Y.B.Com. – Mathematical and Statistical Techniques-II BUBCOMFSII.603Elective CourseSr. No.CourseCodeCredits3T.Y.B.Com. – Computer System and Applications -IBUCCAS506034T.Y.B.Com. – Computer System and Applications -IIBUCCAS60603
B. K. BIRLA COLLEGE OF ARTS, SCIENCE AND COMMERCE(AUTONOMOUS)KALYAN (W)Affiliated to University of MumbaiEvaluation Pattern for F.Y.B.Sc., S.Y.B.Sc. and T.Y.B.Sc.1.INTERNAL ASSESSMENT40 marks1.11.21.3One class test (Objectives/ Multiple Choice)Assignment/ Project/ PresentationActive participation, Overall performance15 marks20 marks05 marks2.EXTERNAL ASSESSMENT (Semester End Examination)60 marksN.B. 1. All questions are compulsory2. All questions carry equal marks.Q.1 Unit-I (with internal option)A.Attempt any two from B, C, D.15 marksB.C.D.Q.2Unit-II (with internal option)A.Attempt any two from B, C, D.15 marksB.C.D.Q.3Unit-III (with internal option)A.Attempt any two from B, C, D.B.C.D.15 marks
Q.4Attempt any threeA.B.C.15 marksD.E.F.1.PRACTICAL ASSESSMENT50 marks1.11.2JournalViva05 marks05 marksN.B. 1. All questions are compulsory2. All questions carry equal marks.Q.1 Attempt any eight MCQ out of 12. (Three Marks each)Based on Unit-1, Unit-2, Unit-3.24 marksQ2. Attempt any two from A, B, C . (Eight Marks Each)Based on Unit-1, Unit-2, Unit-3.16 marksEvaluation Pattern for F.Y.B.Com.1.INTERNAL ASSESSMENT40 marks1.11.21.3One class test (Objectives/ Multiple Choice)Assignment/ Project/ PresentationActive participation, Overall performance15 marks20 marks5 marks2.EXTERNAL ASSESSMENT (Semester End Examination)60 marksN.B. 1. All questions are compulsory2. All questions carry equal marks.Q.1 Unit-IAttempt any TWO out of four sub questions. (6 marks each)Q.2Unit-IIAttempt any TWO out of four sub questions. (6 marks each)12 marks12 marks
Q.3Unit-III and Unit-IV(with internal option)Attempt any TWO out of four sub questions. (9 marks each)Q.4Unit-IV and Unit-V (with internal option)Attempt any TWO out of four sub questions. (9 marks each)18 marks18 marksEvaluation Pattern for T.Y.B.Com.1.INTERNAL ASSESSMENT40 marks1.11.21.3One class test (Objectives/ Multiple Choice)Assignment/ Project/ PresentationActive participation, Overall performance15 marks20 marks5 marks2.EXTERNAL ASSESSMENT (Semester End Examination)60 marksN.B. 1. All questions are compulsory2. All questions carry equal marks.Q.1 Module-I (with internal option)A.15 marksB.Q.2Module-II(with internal option)A.15 marksB.Q.3Module-III(with internal option)A.15 marksB.Q.4A.B.Module-VI(with internal option)15 marks
B. K. Birla College of Arts, Science and Commerce, Kalyan (W.)Syllabus w.e.f. Academic Year, 2018-19 (CBCS)F.Y.B.Sc. Semester- ICalculus ICOURSE CODE: BUSMT101 (2018-19) Credits- 02Objectives: To learn about Real Numbers and the Axiom of CompletenessSequences and Limits of SequencesLimits of Functions and ContinuitySr. No. Units1Real Number System1.1 Real number system and order properties ofLectures (45)15, Absolute valueand its properties.1.2Bounded sets, statement of l.u.b. axioms, g.l.b axioms and itsconsequences, Supremum and Infimum, Maximum andMinimum, Archimedean property and it’s applications, densityof rationals.1.3 AM-GM inequality, Cauchy-Schwarz inequality, Intervals andneighbourhoods, Hausdorff property.215Sequences2.1 Definition of a sequence and examples, Convergent andDivergent sequences, Bounded Sequences, Every convergentsequence is bounded, Limit of a convergent sequence and itsuniqueness. Algebra of convergent sequences, Sandwichtheorem.2.2 Convergenceofsomenamely ./(2.3/ .standard) sequences. /.Monotone sequences, Monotone convergence theorem andconsequences such as convergence of ./ /
2.42.53Subsequences: Definition, Subsequence of a convergentsequence is convergent and it converges to the same limit. Everysequence inhas a monotonic subsequence. BolzanoWeierstrass TheoremDefinition of Cauchy sequence, Every convergent sequence is aCauchy sequence and its converse.15Limits and ContinuityBrief review : Domain and range of a function, injectivefunction, surjective function, bijective function, composite oftwo functions (when defined). Inverse of a bijective function.3.1 Graphs of some standard functions such as( . /intervals of. /). / over suitable.3.2definition of limit of a real valued function of real variable,Evaluation of limit of simple functions using the definition,uniqueness of limit if it exists.3.3Algebra of limits (with proof), Limit of composite functions,Sandwich theorem, Left hand limits and Right hand limits, non( )( ) andexistence of limits,( )3.4Continuity of a real valued function on a set in terms of limits,examples,definition of continuity, Continuity of a realvalued function at end points of domain, Sequential continuity,Algebra of continuous functions, discontinuous functions,examples of removable and essential discontinuity.References:1. R. G. Bartle – D. R. Sherbert, Introduction to Real Analysis, John Wiley & Sons,1994.2. Sudhir R. Ghorpade – Balmohan V. Limaye, A Course in Calculus and RealAnalysis, Springer International Ltd., 2000.
3. S. C. Malik and SavitaArora, Mathematical Analysis, Wiley Eastern Ltd., :Chapter 1, 3, and 5.4. R. R. Goldberg, Methods of Real Analysis, Oxford and IBH, 1964.5. James Stewart, Calculus, Third Edition, Brooks/Cole Publishing Company, 1994.Practicals:1. Application based examples of Archimedian property, Intervals, Neighbourhood.2. Finding upper bound, lower bound, supremum and infimum of finite and infinitesets.3. Calculating limits of sequences.4. Problems on Cauchy sequences and monotone sequences.5. Finding limits of real valued functions, applications of Sandwich theorem.6. Examples of continuous and discontinuous functions.7. Miscellaneous theory questions based on full paper.Algebra ICOURSE CODE: BUSMT102(2018-19) Credits- 02Objectives: To learn about Sr. No.Integers and divisibility of integersFunctions and Equivalence relationsPolynomials.UnitsPrerequisite:Set Theory: Set, subsets, union and intersection of two sets,empty set, Universal set, complement of set, De Morgan laws,Cartesian Product of two sets, Permutation and Combinations .Complex Numbers: Addition and multiplication of complexnumbers, modulus and amplitude, conjugate of complex number,De Moivere’s Theorem11.1Integers and divisibilityStatements of well-ordering property of non-negative integers,Principle of finite induction (first and second) as a consequenceof well-ordering property, Binomial theorem for non-negativeexponents, Pascal Triangle.Lectures (45)15
1.2Divisibility in integers, division algorithm, greatest commondivisor (g.c.d.) and least common multiple ( l.c.m.) of twointegers, basic properties of g.c.d. such as existence anduniqueness of g.c.d. of integers and and that the g.c.d. can beexpressed as, Euclidean algorithm, Primes,Euclid's lemma, Fundamental theorem of arithmetic, The set ofprimes is infinite.1.3 Congruence relation: definition and elementary properties,Euler’sfunction, Statements of Euler’s theorem, Fermat’stheorem and Wilson theorem, Applications.215Functions and Equivalence relations2.1 Definition of a relation, definition of a function, domain, codomain and range of a function, composite functions, examples,( ) of a functionimage ( )and inverse imageInjective,surjective, bijective functions, Composite of injective, surjective,bijective functions when defined.2.22.32.43Invertible functions, Bijective functions are invertible andconversely, Examples of functions including constant, identity,projection, inclusion, Binary operation as a function, properties,examples.Equivalence relations, Equivalence classes, properties such astwo equivalences classes are either identical or disjoint,Definition of partition of a set, every partition gives anequivalence relation and vice versa.Congruence modulo is an equivalence relation on , Residueclasses, Partition of, Addition modulo , Multiplication .modulo , examples such as , - *Polynomials3.1 Definition of polynomial, polynomials over the field, whereAlgebra of polynomials, degree of polynomial,basic properties.3.2Division algorithm in , - (without proof) and g.c.d. of twopolynomials and its basic properties (without proof), Euclideanalgorithm (without proof), applications, Roots of a polynomial,15
relation between roots and coefficients, multiplicity of a root,Remainder theorem, Factor theorem.3.3Complex roots of a polynomial in , - occur in conjugatepairs, Statement of Fundamental Theorem of Algebra, Apolynomial of degree in , - has exactly complex rootscounted with multiplicity, A non constant polynomial in , can be expressed as a product of linear and quadratic factors in, -, Necessary condition for a rational number to be a rootof a polynomial with integer coefficients, simple consequencessuch as is an irrational number where is a prime number,roots of unity, sum of all the th roots of unity.References:1. David M. Burton, Elementary Number Theory, Seventh Edition, McGraw HillEducation (India) Private Ltd.2. Andre Weil, Very Basic Number Theory.3. Norman L. Biggs, Discrete Mathematics Second Edition, Oxford University Press,USA.4. Niven and S. Zuckerman, Introduction to the theory of numbers, Third Edition,Wiley Eastern, New Delhi.5. G. Birkhoff and S. Maclane, A Survey of Modern Algebra, Third Edition,MacMillan.6. Kenneth Rosen, Discrete Mathematics and its applications, Mc-Graw HillInternational Edition, Mathematics Series.7. Lindsay N. Childs, Concrete Introduction to Higher Algebra, Springer.8. J. Stillwell, Element of Algebra, Springer.Practicals1. Mathematical induction Division Algorithm and Euclidean algorithm in Primesand the Fundamental theorem of Arithmetic.2. Convergence and Euler’s-function, Fermat’s little theorem, Euler’s theorem andWilson’s theorem.3. Functions ( direct image and inverse image), Injective, surjective, bijectivefunctions,4. Finding inverses of bijective functions. Equivalence relation.
5. Factor Theorem, relation between roots and coefficients of polynomials,6. Factorization and reciprocal of polynomials.7. Miscellaneous theory questions based on full paper.F.Y.B.Sc. Semester- IICalculus IICOURSE CODE: BUSMT201 (2018-19) Credits- 02Objectives: To learn about Continuity of real valued functionsDifferentiability of real valued functions and its ApplicationSeries of real numbersSr. No.Units1Continuity of a function on an intervalReview of the definition of continuity ( at a point and on the domain).1.11.22Lectures(45)15Properties of Continuous functions:(1) Intermediate value theorem (with proof) and its applications.(2) A continuous function on a closed and bounded interval isbounded and attains its bounds.(3) If a continuous function on an interval is injective then it isstrictly monotonic and inverse function is continuous and strictlymonotonic.Definition o
Syllabus Structure: 1. In F.Y.B.Sc. (CBCS) in Semester I and II, there will be two papers each with 2 credits and one practical of 2 credits in each semester 2. In S.Y.B.Sc (CBCS) in Semester III and Semester IV, there will be three papers
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ACKNOWLEDGEMENT SLIP (To be filled in by the Investor) TRANSMISSION REQUISITION FORM PAN No Collection Centre / ABSLAMC Stamp & Signature Aditya Birla Sun Life AMC Limited (Investment Manager to Aditya Birla Sun Life Mutual Fund) (Formerly known as Birla Sun Life Asset Management Company Limited) Regn. No.: 109.
BIRLA INSTITUTE OF TECHNOLOGY & SCIENCE PILANI (RAJASTHAN) MEMBERS OF THE BOARD OF GOVERNORS Dr. Kumar Mangalam Birla, Chancellor Smt. Shobhana Bhartia, Pro-Chancellor
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