Introduction for the Course M.Sc. (Industrial Mathematics with Computer Applications) course syllabus is revised to cater to the needs of credit based-semester and grading system. The changing scenario of higher education in India and abroad is taken into consideration to make this syllabus more oriented towards the applications of Mathematics and Computer Science in Research and Industry. The syllabus encompasses the subjects related to Industrial Mathematics, Core Computer Subjects as well as the Emerging Technologies in Computer Science. Theory Courses will create the foundation for the development of logical thinking and the Practical Courses gives hands on experience towards the Industrial Requirements. Taking into consideration the rapid changes in science and technology and new approaches in different areas of Mathematics and related subjects, Board of Studies in Mathematics with consent of teachers of Mathematics and Computer Science from different colleges affiliated to University of Pune has prepared the syllabus of M.Sc. (INDUSTRIAL MATHEMATICS WITH COMPUTER APPLICATIONS). To develop the syllabus the U.G.C. Model curriculums followed. Aims: (i) Give the students sufficient knowledge of fundamental principles, methods and a clear perception of the innumerous power of mathematical ideas and tools and knowledge of how to use them by modeling, solving and interpreting. (ii) Reflecting the broad nature of the subject and developing mathematical tools for continuing further study in various fields of science. (iii) Enhancing students’ overall development and to equip them with mathematical modeling abilities, problem solving skill, creative talent and power of communication necessary for various kinds of employment (iv) Enabling students to develop a positive attitude towards mathematics as an interesting and valuable subject of study. Objectives: (i) A student should be able to recall basic facts about mathematics and should be able to display knowledge of conventions such annotations, terminology and recognize basic geometrical figures and graphical displays, state important facts resulting from their studies. (ii) A student should get a relational understanding of mathematical concepts and concerned structures, and should be able to follow the patterns involved with mathematical reasoning. (iii) A student should get adequate exposure to global and local concerns so as to explore many aspects of Mathematical Sciences. (iv) Students should be able to apply their skills and knowledge, that is, translate information presented verbally into mathematical form, select and use appropriate mathematical formulae or techniques in order to process the information and draw the relevant conclusion. (v) A student should be made aware of history of mathematics and hence of its past, present and future role as part of our culture. (vi) A student should be able to write necessary algorithms and programs in different languages as per the need of the industry Eligibility: Students from any graduation (with Mathematics up to second year 4) securing a minimum of 50% marks. Student Registration: Except the credits for practical Courses, where ever applicable, a student can register for less number of courses in a Semester subject to the condition that such a student will have to complete the degree in a Maximum of 5 years for 3 Years program Structure of the Course Semester I T/P Code Course Title % of Total Hours/week Credits Assessment IA UE T MIM Real Analysis 50 50 100 4 4 101 T MIM Linear Algebra 50 50 100 4 4 102 and computational Geometry T MIM Discrete 50 50 100 4 4 103 Mathematical structures T MIM C Programming 50 50 100 4 4 104 T MIM Elements of 50 50 100 4 4 105 Information Technology P MIM Lab Course 50 50 100 4 4 106 based on MIM 104 T/P: Theory/Practical Semester II T/P Code Course Title % of Assessment Total Hours/week Credits Marks IA UE T MIM Complex 50 50 100 4 4 201 Analysis T MIM Algebra II 50 50 100 4 4 202 T MIM Numerical 50 50 100 4 4 203 Analysis T MIM Object oriented 50 50 100 4 4 204 Programming with C ++ T MIM Data structures 50 50 100 4 4 205 using C P MIM Lab Course 50 50 100 4 4 206 Semester III T/P Code Course Title % of Marks Hours/week Credits Assessment IA UE T MIM 301 Topology 50 50 100 5 5 T MIM 302 Design And 50 50 100 5 5 Analysis of algorithm T MIM 303 Object 50 50 100 5 5 Oriented Software Engineering T MIM 304 Operating 50 50 100 5 5 Systems T MIM 305 Database 50 50 100 5 5 Fundamentals P MIM 306 Lab Course 50 50 100 5 5 based on MiM-304 and MIM-305 Semester IV T/P Code Course Title % of Total Hours/week Credits Assessment Marks IA UE T MIM 401 Ordinary 50 50 100 5 5 differentia equations T MIM 402 Coding Theory 50 50 100 5 5 T MIM 403 Computer 50 50 100 5 5 Networks T MIM 404 Programming 50 50 100 5 5 in PHP T MIM 405 JAVA 50 50 100 5 5 programming P MIM 406 Lab Course 50 50 100 5 5 based on MiM-405 and MIM-404 Semester V T/P Code Course Title % of Total Hours/week Credits Assessment Marks IA UE T MIM 501 Theoretical 50 50 100 5 5 Computer Science T MIM 502 UNIX 50 50 100 5 5 T MIM 503 .NET 50 50 100 5 5 T MIM 504 ELECTIVE 50 50 100 5 5 P MIM 505 Lab work based 50 50 100 5 5 on MIM-502 and MIM-503 Examination pattern: Each course will have: 50% marks for internal (i.e. in-semester) assessment. 50% of marks for semester-end examination conducted by University of Pune. The student has to obtain forty percent marks in the combined examination of In- Semester assessment and Semester-End assessment with a minimum passing of thirty percent in both these separately. Theory examination: Internal examination: At least one internal assessment must be conducted for the one credit course. (Four tests for four credits course).Each credit will have an internal (continuous) assessment of 50% of marks and a teacher must select a variety of procedures for examination such as: 1) Written Test and/or Mid Term Test (not more than one or two for each course) 2) Term Paper 3) Journal/Lecture/Library notes; 4) Seminar presentation; 5) Short Quizzes; 6) Assignments; 7) Extension Work; 8) An Open Book Test (with the concerned teacher deciding what books are to be allowed for this purpose ) External Examination Theory examination will be conducted for a period of maximum 45 minutes for each credit. University Practical examination: Practical examination will be of the same duration as that of the practical exercises for that course. There shall be 10 marks for laboratory log book and journal, 10 marks for viva-voce. For practical course of four credits at least three experiments should be asked. For the course of two/ three credits at least two experiments and for the course of single credit one experiment should be asked. Certified journal is compulsory for appearing for practical examination. There shall be two experts and two examiners per batch for the practical Examination. One of the examiners will be external. Internal Continuous Assessment Process for the Practical The number of practical Assignments will be decided by the Course Faculty which covers all the Course Contents. Following are some Evaluation Criteria’s 1) Journal Assessment. 2) Viva-voce at the time of submission of each practical 3) Group discussion of 5/6 students for testing the understanding level of a student 4) Additional practical work of interdisciplinary approach 5) Attendance- 5 Marks Practical Attendance Practical attendance percentage Marks 75%-80% 1 Mark 81%-85% 2 Marks 86%-90% 3 Marks 91%-95% 4 Marks Above 95 % 5 Marks MIM-601 FULL TIME INDUSTRIAL TRAINIG /INDUSTRIAL PROJECT Period – Minimum 4 months 1. There will be a teacher coordinator for a group of students. A teacher coordinator will take care of joining letters from students along with other necessary submission listed below. 2. A student will have to submit 2 reports during the period of ITP to the Department of the college. 3. After the completion of the ITP, a student will have to submit a synopsis along with the project completion certificate from the respective industry/research institute /educational institute. 4. A student will submit one hard copy (Student Copy) and a soft copy’s (preferably 2 CDs) of the work carried out towards ITP. 5. The project will be graded by the experts (One internal examiner, one external examiner(academic expert) and one industrial expert) as follows: O – 75 and above C– 50 and above F- A student will have to A – 65 and above D– 45 and above carry out project once again for a B – 55 and above E– 40 and above complete semester Important Note: A student can complete ITP with a research project of a teacher / an expert funded by the University of Pune/ a funding agency. Evaluation for internal 50 Marks will be done according to Progress Report written by Teacher Coordinator Evaluation for external 50 Marks will be done by Industrial Expert, Academic Expert and One Internal Examiner. ------------------------------------------------------------------------------------------------------------ M. Sc. (Industrial Mathematics with Computer Applications) From the Academic Year 2015-16 M. Sc –III Semester V MIM 501: Digital Image Processing UNIT 1. Introduction [3]  What is Digital Image Processing?  The origins of Digital Image Processing  Examples of Fields that use Digital Image Processing  Gamma-Ray Imaging  X-Ray Imaging  Imaging in the Ultraviolet Band  Imaging in the Visible and Infrared Bands  Imaging in the Visible and Infrared Bands  Imaging in the Visible and Infrared Bands  Imaging in the Microwave Band  Imaging in the Radio Band   Fundamental steps in Digital Image Processing  Components of an Image Processing System UNIT 2. Digital Image Fundamentals [6]  Elements of Visual Perception  Light and the Electromagnetic Spectrum  Image sensing and Acquisition  Image Sampling and Quantization  Some Basic Relationships between Pixels  An Introduction to the Mathematical Tools Used in Digital Image Processing  Array versus Matrix Operations  Linear versus Nonlinear Operations  Arithmetic Operations  Set and Logical Operations  UNIT 3. Intensity Transformation and Spatial Filtering [7]  Background  Some Basic Intensity Transformation Functions  Histogram Processing  Histogram Equalization  Histogram Matching (Specification)  Local Histogram Processing   Fundamentals of Spatial Filtering 1  Smoothing Spatial Filters  Sharpening Spatial Filters  Combining Spatial Enhancement Methods UNIT 4. Filtering in the Frequency Domain [10]  Background  Preliminary Concepts  Sampling and the Fourier Transform of Sampled Functions  The Discrete Fourier Transform (DFT) of One variable 5 Extension to Functions of Two Variables  Some Properties of the 2-D Discrete Fourier Transform  The Basics of Filtering in the Frequency Domain  Image Smoothing Using Frequency Domain Filters  Image Sharpening Using Frequency Domain Filters  Selective Filtering  UNIT 5. Image Restoration and Reconstruction [6]  A Model of the Image Degradation / Restoration Process  Noise Models  Restoration in the Presence of Noise Only- Spatial Filtering  Periodic Noise Reduction by Frequency Domain Filtering  Band reject Filters  Band pass Filters  Notch Filters  Estimating the Degradation Function  Inverse Filtering  Minimum Mean Square Error(Wiener) Filtering  Geometric Mean Filter UNIT 6. Morphological Image Processing [5]  Preliminaries  Erosion and Dilation  Opening and Closing  The Hit-or-Miss Transformation  Some Basic Morphological Algorithms  Boundary Extraction  Hole Filling  Extraction of Connected Components  Convex Hull  Thinning  Thickening  Skeletons  Pruning 2  Morphological Reconstruction UNIT 7. Image Segmentation [6]  Fundamentals  Point, Line, and Edge Detection  Background  Detection of Isolated Points  Line Detection  Edge Models  Basic Edge Detection  Edge Linking and Boundary Detection  Thresholding  Foundation  Basic Global Thresholding  Optimum Global Thresholding Using Otsu's Method  Using Image Smoothing to Improve Global Thresholding  Using Edges to Improve Global Thresholding  Region-Based Segmentation UNIT 8. Representation and Description [5]  Representation  Boundary (Border) Following  Chain Codes  Polygonal Approximations Using Minimum-Perimeter Polygons  Other Polygonal Approximation Approaches  Signatures  Boundary Segments  Skeletons  Boundary Descriptors  Some Simple Descriptors  Shape Numbers  Fourier Descriptors  Regional Descriptors  Some Simple Descriptors  Topological Descriptors  Texture Text Book: 1. Gonzalez, R. C. and Woods, R. E. [2002/2008], Digital Image Processing, 3rd ed., Prentice Hall Reference Books: 3