Bsc MPC

MATHEMATICS (B.A. and B.Sc.) - Paper III – Mathematics

Unit A: Rings & Fields:
Definition and examples of a ring. Simple properties. Types of rings. Integral domain, skew field, field. Examples. Homomorphism of rings, properties, ideals Maximal ideal, Prime ideal. Quotient rings. Theorem. If R is a commutative ring with identity and M is an ideal of R, then

2. M is a maximal ideal if & only if R/M is a field. 3. M is a prime ideal of a ring R ff & only ff R/M is an integral domain. Definition of Euclidean Ring. Examples. The ring of Gaussian integers. Polynomial rings. Ring of polynomials over a field. Division algorithm.

Unit B : Linear Algebra :
Vector space definition and examples of subspace, quotient spaces, linean dependence and independence, basis, dimension, finite dimensional vector spaces invarience of the number of vectors in basis. Linear transformations, kernel of a linear transformation, rank and nullity of a linear transformation. Rank and nullity theorem.

Algebra of linear transformations introduction of addition and scalar multiplication and multiplication of Linear transformations. Characteristic roots, characteristic equation. Matrix of Linear transformation relative to a basis, change of the representation of the matrix wfth the basis. Similar matrices. Eigen values, eigen vectors, Cayley Hamilton Theorem. Inverse of matrix using Cayley Hamitton Theorem. Elemantary transformation and matrices, invarience, rank reduction to normal form, computation of inverses of matrices.

System of Homogeneous and non homogeneous linear equation consistence conditions, general solution. Inner product spaces norm of a vector space. Schwart inequality. Orthogonal vectors. Orthonormal vectors. Bessel inequality. Perseval's equation. Gram Schmidt orthogonalization process. Real quadratic forms, reduction of quadratic forms under general linear and orthogonal groups of Linear transformation. Sylvesters Law of Inertia definite, semi definite norms. Necessary and sufficient conditions for definiteness general reduction of 2nd degree equation in 2 and 3 variables.

Reference Books
1. Hoff man and Kunz : Linear Algebra
2. Herstein, I.N. : Topics in Algebra.
3. Telugu Adademi.
4. L. Nagamuni Reddy.
5. V Krishna Murthy & J.L. Arora Linear Algebra.
6. Sharma & Vasistha Linear Algebra.
7. A first course in abstFact algebra Fraleigh Telugu translation by Telugu Akademi.
8. Bhattacharya and Jain Rings and Fields.
9. Surrjeet Singh and Zammenuddin Modern Algebra.
10. A.G. Gardner Grop Theory

(For Mathematics Students)

Paper III - Electromagnetics & Electronics

Practicals - Paper III

Paper IV - Modern Physics

(For non-Mathematics Students)

Paper - III Electricity, Magnetism & Electronics

Paper IV - Modern Physics

(For Mathematics Students)

PHYSICS - Paper III - Electromagnetics & Electronics (for Mathematics students)

1.Electrostatics : Coulomb's law. MKSA system of units - charge distributions - discrete and continuous. Electric field. The scalar potential. Field and potential due to a dipole : due to N discrete point changes : due to continuous change distribution. Potential of a long charged wire. Potential of a uniforily charged circular disc. Gauss law (integral and differential forms). Applications : Electric field due to an infinite sheet of charge, field due to a spherical distribution of charge at points within and outside the sphere.

2. Conductors : Conductor as an equipotential surface. Field near the surface of a conductor. Field near a charged conducting planed. Field near a conducting spherical shell, capacitance of a parallel plate capacitor, of a concentric spherical shell and of a sphere. Electrostatic energy of a charged capacitor.

3. Dielectrics : Origin of polarisation, Polarisation, charge - density Electric field due to polarisation - Relation between D.E. and P. Dielectric constant and Electric susceptibility. Gauss law in the presence of dielectrics. Boundary conditions on D and E. Capacitance of a capacitor with a dielectric. Energy density within a dielectric. Dielectric breakdown.

4. Steady Currents : Current density. Equation of continuity, surface current density, Electrical conductivity and Ohw's law, EMP, Energy dissipation, reciprocity theorem, Kirchhoff's laws. Mesh and Node analysis. Superposition principle. Thevenin and morton theorems.

5. Magnetostatics : Definition of B - Biotsavart law - Divergence of B. Magnetic flux - the Surface integral of B. B due to a long straight current. Ampere's law (integral and differential forms). B along the axis of a circular loop carrying current. Field due to Helmholtz coils. Force on a current element due to a field B. Force between two parallel wires carrying currents. Definition of Ampere. Torque on a current loop. Moving coil galvanometre. The solenoid and the toroid. Motion of a charged particle in a uniform magnetic field. Helical path, focussing action and Hall effect. Motion of charged particles in electric and magnetic fields.

6. Electromagnetic Induction: Taraday's law (integral and diff erential forms), Lenz's law, expression for induced EMF Time-varying magnetic fields - Betatron - Self induction. Self inductance of a long straight wire and a sole.noid. Mutual induction. Coefficient of coupling. Inductance and magnetic energy.

7. Magnetic Fields in Matter : Para, dia and ferro magnetic substances, Magnetisation, Relation between 8, M and H. Definition of H, Magnetic susceptibility, Hysterisis. B-H curve, Y Ferromagnetism. Magnetic domains, Boundary conditions on B and H. The magnetic circuit.

8. Varying and Alternating Currents : Circuit with L and R, charging and discharging of a capacitor through R, Discharge of a capacitor through L. Series LCR circuit. Sinusoidal voltage applied to (i) a resistance (ii) and inductrance andd (iii)) across a capacitance. Phasors and phase diagrams. Use of complex numbers. Reactance and impedance. Inductive and capacitive reactances - power factor -LCR circuits - Series resonant circuit - Q factor - Parallel resonant circuits - Generators, Motors and Transformers (Principles only).

9. Maxwell's Equations : Review of basic laws of Electricity and Magnetism. Displacement current. Ampere's law in general form. Maxwell's equations. Plan EM waves, Transverse nature of EM waves, Energy density, energy flow (poynting vector).

10. Electronics : Diodes : Junction diode - Volt ampere characteristics. Half wave rectifier, Full wave rectifier and Bridge rectifier - Ripple factor - Capacitive and inductive filters. (Qualitative). Zener diode, its characteristics. Transistors, working of a transistor, currents in a transistor, DC Alpha, CB, CC and CE configurations, characteristics of CE configuration. CE amplifier, biasing, voltage divider bias, single stage R.C. couple amplifier - graphical analysis only. Oscillators : Positive feedback amplifier as oscillator - Barkhausen criterion, phase shift oscillator. Modulation and detection : Amplitude modulation. Frequency modulation -Demodulation using diodes - Elementary principles of radio transmission and reception.

Digital Electronics : Binary arithmatics, and or, not gates using discrete components. Truth tables - NAND, NOR and ZOR gares half adder and full adder. De Morgan's theorems - RS Flipflot counters registers and memory elements.

Textbooks Recommended
1. Electricity and Magnetism by Mahajan and Rangawala (TMH)
2. Basic Electronics and Linear Circuits by Bhargawa, Kulashrashta and Gupta (TT 11, Chandigarh)
3. Digital principles and applications by Malvino and Leach (TMN)

Books Recommended for Supplementary Reading
1. Physics II by Halliday and Resnick (Siley Eastern)
2. Electricity and Magnetism by D.N. Vasudeve (S Chand)
3. Electronic Fundamentals and applications by John D. Ryder (DHI)

PHYSICS - Practicals - Paper III

1. Determination of constant of B.G.
2. Determination of M & H using Deflection and vibration magneto meters.
3. Study of Magnetic field along the axis of a circular coil-steward and Geo's apparatus.
4. Measurement of low resistance and resistivity carry Foster's Bridge.
5. Temperature coefficient of resistance by Caey Foster's Bridge.
6. Calibration of Voltmeter (low and light range with potentiometer.
7. Calibration of Ammeter using potentiometer
8. Plotting of charging and discharging of a capacitor through resistance.
9. Series and paralles resenacacircuit measurement of 'Q'
10. Impeclence and power factor of an AC circuit.
11 I-H curve hysterisis loss of a magnetic material.
12. Determination of AC frequency by Sonometer.
13. Determination of e/m by Thomson's method.
14. Design of a Multimeter (Conversion of a galvanometer to voltmeter and ammeter)
15. Determination of Rydberg's constant using Hydrogen spectrum.
16. Verification of Network theorems -Thevinin's, Norton's theorems and Maximum power Transfer Theorem.

PHYSICS - Paper IV - Modern Physics (For Mathematics Students)

Millikan's method - Mass of the Electron - Avpgadro's number - Mass of the Hydrogen atom.

Aston's mass spectrography - Bainbridge's mass spectrography - Atomic mass unit - Mass defect - Packing fraction and binding energy.

Spectroscopy - Bohr's theory of hydrogen atom - Energy level diagrams correction for the finite mass of the nucleous -spectrum of the singly jonised helium - Discovery of deuterium - Sommerfield's eliptic orbit theory - Relativistic correction for elliptical orbits - the Fine-structure of special lines - vector model of the atom - spatial quantisation -quantum numbers associated with the vector model - Total angular momentum of the atom - Coupling schemes -Pauli's exclusion principle - Periodic classification of elements - Spectrum notation Selection roles - spectrum of Sodium D - lines - Zeeman eff ect and its explanation - Paschen - Bach effect - Stern and Gerlach experiment -Elements of band spectra - Elementary treatment of Raman effect.

Absorption of X-ray - Photoelectric effect - Neyon's Experiment compton effect, explanation, theory and experiment wave nature of matter - De Broglie's concept of matter - waves Expression for De Broglie's wavelength - Electron diffraction - Davisson and Gormer experiment - G.P. Thomson experiment Electron Microscope - Heisemberg's uncertainty Principle - postulates of quantum Mechanics - Schrodinger wave equation wave function - Time independent wave equation - operators - Eigen values and eigen functions - Application to infinitely square well, potential step and barrier.

Detection and measurement of radioactive radiation - Wilson's cloud chamber - G.M. Counter.

Rutherford's theory of scattering of aipha particles by heavy nuclei - experimental confirmation - Range - energy relation-a-emission - Garnow's theory of alpha decay characteristics of beta ray spectra - Relation between energy and momentum - elementary theory - Nuclear origin of beta particles.

Gamma radiation - qualitative explanation of gamma ray interaction with matter.

Rutherford's experiment of nitrogen disintegration by protons - Artificial radioactivity. Transuranic elements - Structure and properties of the nucleous size, charge and mass - Nuclear forces - binding energy curve - Liquid drop model -Emiempirical mass formula - Nuclear stability - particle accelerators cyclotron and synchro - cyclotron.

Cosmic rays - Nature Properties - Effect of Latitude, longitude and altitude - Discovery of position - elementary particles and their classification.

X-ray diffraction by crystals - Bragg's law - Lane's equations KCI and NaCl structures - Electron and neutron diffraction - Classification of magnetic materials - Dia, para and ferro-magnetism - Langevin's theory of para-magnetism - Gerromagnetic domains Weises theory of ferromagnetism - Curic - Weiss Law.

Super conductivity - Experimental observations - Lasers - spontaneous and stimulated emission - population inversion - He-Ne and Ruby lasers - semiconductor laser.

Books
1. Atomic Physics - JB. Rajan;
2. Introduction to Modern Physics Ritchmeyer and Kennaw;
3. Nuclear Physics -Kaplan;
4. Atomic Spectra White;
5. Elements of Quantum Mechanics - Strance;
6. Modern Physics Beesev;
7. Physics of Atom - Weiner
8. Physics of Atom - Wehr and Richards

(For non-Mathematics Students)

PHYSICS - Paper IV - Modern Physics (For Non-mathematics Students)

1. Atomic nature of matter : Discovery of electron, Determination of e. mass of an election, Avegadrors number.

2. Positive Rays : Thomson's apparatus for determination of E/M mass spectrograph (Bambridge).

3. Radio activity Natural Radio active emissions, the law of Radioactive isotopes tracers - studies of metabolic uptake - Transport studies - Chrowsome division - Istopic dilution - Location of herporrage - Radio cardiography -Nonradio active tracers - Radio therapy - Radiation directors Geiger counter cloud chamber and bubble chamber -Photo-multiplier tube.

4. Rutherford - Bohratom models, Rutherford Model, Size of the nucleus Bohr's theory of the atom victor model of the atom Spatial quantization - Spinning electron - Quantum numbers associates with the Vector model - L.S. Coupling -Pauli's excusion principle - periodic - classification of elements.

5. Quantum Theory : Photoelectric affect, Millkan's experiment for verifying Einstein's equation Compton effect -Experimental verification of the formula - Raman effect, its explanation and molecular structure.

6. X-rays production, X-ray spectra, Morley's law, absorption of X-rays Medical and biological application of radiation -Radiation hazards and protection - Radiation hazards In space flight X-ray diffraction - Laue's experiment Bragg's Law -Bragg's spectrometer Nacl and KcI crystal structure - Electron diffraction.

7. Nucleus: Discovery of the Neutron - nuclear binding energy - Nuclear fission and fusion - Energy equation in nuclear reactions - Isotopes, isomers, isobars and istones - Trans - Uranic elements.

8. Cosmic Rays: Early experiments - Directional effects - Altitude and latitude effect - Van Allen Belts - Elementary Practicals and their nature.

9. Earth's Magnetism: Earth's magnetic elements, Diapara Ferromagnetism characteristics - Magnetic domains forferromagnetism -Anie's law and curie - Coeiss Law (Statements) Bohr magneton - its significance Zeeman effect qualitative treatment.

Books
1. Atomic Physics by J.B. Rajan;
2. Physics for Biology and Premedical Students Desmond M. Buns and Simon G.G. Macdonald.
(Physics Practicals are common for mathematics and non-Mathematics Students.)

IInd Year

Paper III - Programming in C++ and Data Structures

IIIrd Year

Paper IV - Business Data Processing

Paper IV - PC Software and Database Management Systems

IInd Year

B.Sc Course Structure and Scheme of Examination

1

Programming in C++ and Data Structures

2.

Programming in C++ and Data Structures Lab

Second Year B.Sc Breakup of marks for Practical

Each student has to answer one question.
The breakup of marks is as follows

1.

Programming in C++ and Data Structures

1. Alogrithms/Problem Solving (10 marks)
2. Programming (10 marks)
3. Result (10 marks)

2.

Viva Voce

10 marks

3.

Record

10 marks

Paper II: Programming in C++ and Data Structures

Unit I
Introduction to C++ - Basics - Procedural Abstraction and Functions

Unit II
I/O Streams - Classes and Abstract Data Types - Flow of Control - Tools for defining ADTs

Unit III
Arrays - Strings and Three Dimensional arrays - Pointers and Dynamic Arrays - Recursion

Unit IV
Templates and Abstraction - Pointers and Linked Lists - Inheritance

Unit V
Data Structures - Linked Lists - Stacks - Queues (Creation, Insertion and Deletion of Nodes) - Trees (Creation, Insertion and Deletion of nodes, in order, preorder and post order traversal) - graphs (adjacency lists, adjacency matrix, depth first search methods)

Laboratory-II: C++ and Data Structures Laboratory

1. Abstract Data Types for Rational numbers and for Complex Numbers (See Example 5 and 6 Page 50-508 for Book 1)

2. Multi Dimensional Arrays (Two Dimensional Grading Problem Page 613 of Book1)

3. Palindrome Testing Program (Page 629 of Book 1)

4. Multipath Inheritance and Virtual Functions Examinations Database (See Page 534 of Book 3)

5. Multilevel Inheritance - Product Company Modeling (see Page 544 of Book 3)

6. Hierarchy Inheritance - Vehicle Database (Page 549 of Book 3)

7. Template Functions for Bubble Sort

8. Program to Demonstrate use of class template that needs a list of values (For details see Programming Examples on Page 766 of Book 1)

9. User Defined Template arguments - Student Record (See Page 609 of Book 3)

10. Overloading of Operators +=, -+, /+ for complex classes.

11. Inheritance of Class Template - Union of sets (see Page 617 of Book 3)

12. Program to perform stack operations such as push() and pop() functions using an array method

13. Program to perform queue operations such as qstore(), qdelete() functions using an array method

14. Program to create the circular queue by using the operations qstore(), qdelete() functions using an array method

15. Program to create the linear linked list and display the list in LIFO method

16. Program to add new companion to a linked list or delete existing components in it.

17. Program to construct a linear linked list and to display the list in FIFO method.

18. Program to convert an infix expression to post fix expression using a stack

19. Program to construct to double linked list and add or delete an item

20. Program to create a binary tree and to display the contents of the tree using the tree traversal methods

21. To implement binary search and calculate the search time.

22. Stream computations with files - student files - creating - writing – reading

Suggested Text Books for Second Year

Prescribed Text Books

1.

Problem Solving with C++

Walter Switch

Addission Wesley

2.

Data Strucutres, Algorithms and Application in C++

Sartanj Sahni

McGraw Hill

Reference Text Books

3.

Mastering C++

R Venugopal, Rajkumar & T Ravishankar

Tata McGrawHill

4.

Data Structures using C++

Yedidjah Langsan, Moshej Augenstin, Aaron M Tanenbaum

Prentice-Hall

COMPUTER SCIENCE - Paper IV - Business Data Processing
Unit I: Introduction to Data Processing concepts, data preparation, transcription, validation, storage and retrieval. Structure of COBOL Programs Four divisions of COBOL, Structured Programming Concepts. Identification, Environment and Data Divisions, Record and Data item descriptions

Unit II : Procedure Division - Data movement verbs, Accept and Display arithmetic verbs, structured programming constructs such as Perform and IF, Table handling, other miscellaneous verbs.

Unit Ill : File Processing - File structure, operations on files, batch processing of sequential files, sorting and merging. Direct access devices, indexed sequential files, relative files.

Unit IV: Overview of systems analysis and design, business system concepts, system development life cycle, project selection, feasibility study.

Unit V : Systems requirements specification and analysis, system design objectives, design, testing and implementation, performance and acceptance criteria.

COMPUTER SCIENCE - Textbooks

1. Philippakis As and Kazmier LJ Information Systems through COBOL McGraw-Hill. 1978.
2. Lee Introduction to Systems Analysis, NIC Galgotia

COMPUTER SCIENCE - Practical Ill - COBOL and D Base/Fox Base/ Fox Pro

COBOL: At least 10 experiments (Programs) on the following :
Structural programming, sequential file creation, file extension, sorting and merge of files, accessing records in a sequential file, operations on direct access fit's, file creation, inserting records, deleting records, start reading from a specified location, Updating files.

D Base or Foxbase or Fox Pro : At least 8 experiments on the following
Building a data base, searching a database, sorting a data base editing and modifying data bases, creating and printing formatted reports, managing numbers and dates, managing multiple data files, designing and developing programs in Dbase/Foxbase/Foxpro. At least 4 experiments on usage of other PC packages such as Lotus etc.

COMPUTER SCIENCE - Practical IV : Project Work
Design and implementation of one of the computer applications

COMPUTER SCIENCE - Paper IV - PC Software and Database Management Systems

Unit I : Introduction to MS-DOS, files, directories, system commends, redirection, pipes, batch files. Wordprocessing (e.g. Word Star) - Features of word processing, creation and editing, global search and replace, formatting block operation mail merge, spell checking.

Unit II: Unix-Login, Unix Commands, System calls, Redirection, pipes File Systems and Operation, Elements of shell programming, sorting.

Unit III : Spread Sheats (Lotus-123) - Worksheet, constants and formulas Library functions, Graphic output, macros, applications.

Unit IV : Relational Database, Structure, storage organisation, relational algebra, Normal forms.

Unit V : D base-III - creation and editing of Dbase files, queries, sorting and indexing, report generation, Dbase-111 programming.

COMPUTER SCIENCE - Textbooks
1. PC Software, made simple Taxali, TMH Press 1994.
2. Richard W. Brightman, Teffrey M. Dimsdale Using Micro Computers, Galgotia, 1987.
3. C.J. Date An introduction to Database ststems - Vol. I (Chapters 1-4, 12-14) Nar osa 1981.