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B.E. (Artificial Intelligence and Data Science) Mathematics for Computer Engineering Syllabus - Mumbai University 2026

This is the SY BE AI and DS syllabus under NEP 2020, in force from the academic year 2025-26. The third and fourth years of this degree are still taught on the earlier CBCS REV-2019 'C' Scheme, because the University has published no NEP syllabus for Semesters V to VIII of any engineering branch.

Mathematics for Computer Engineering.pdf
Semester 3 · SY BE AI and DS · NEP 2020

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Syllabus for Mathematics for Computer Engineering

Semester 3 · SY BE AI and DS · NEP 2020

Module 0: Prerequisite

  • Complex Numbers, Probability, Central tendencies and dispersion in Statistical techniques, Baye’s theorem, Random variable, Discrete and Continuous random variables.

Module I: Linear Algebra (Theory of Matrices ) 5 hours

  • 1 Characteristic Equation, Eigenvalues and Eigenvectors, and properties (without proof)
  • 2 Cayley-Hamilton Theorem (without proof), verification and reduction of higher degree polynomials
  • 3 Similarity of matrices, diagonalizable and non-diagonalizable matrices Self-learning Topics: Derogatory and non-derogatory matrices, Functions of Square Matrix, Linear Transformations, Quadratic forms.

Module II: Linear and Non-Linear Programming Problems 5 hours

  • 1 Types of solutions, Standard and Canonical of LPP, Basic and Feasible solutions, slack variables, surplus variables, Simplex method.
  • 2 NLPP with one and two equality constraint (two or three variables) using the method of Lagrange’s multipliers Self-learning Topics: Sensitivity Analysis, Big-M method, Artificial variables, Kuhn-Tucker conditions

Module III: Modular Arithmetic 4 hours

  • 1 Introduction to Congruence, Linear congruence, reminder theorem, solving polynomials, system of linear congruence
  • 2 Eluer’s theorem, Fermat’s little theorem, Application of congruence-RSA algorithm. Self-learning Topics: Divisiblility, GCD, properties of prime numbers, fundamental theorem of arithmetic.

Module IV: Fourier Series 4 hours

  • 1 Dirichlet’s conditions, Fourier series of periodic function with period 2π and 2l.
  • 2 Fourier series of even and odd functions. Self-learning Topics: Orthogonal and orthonormal set of functions, Complex form of Fourier Series, Half range Sine and Cosine Series.

Module V: Statistical Techniques 4 hours

  • 1 Karl Pearson’s coefficient of correlation (r).
  • 2 Spearman’s Rank correlation coefficient (R) (with repeated and non-repeated ranks).
  • 3 Lines of regression, fitting of first-degree curves. Self-learning Topics: Covariance, Fitting of second-degree and exponential curve.

Module VI: Probability 4 hours

  • 1 Moment generating function, Raw moments.
  • 2 Poisson Distribution, Normal Distribution Self-learning Topics: Skewness and Kurtosis of distribution (data), types of distribution and their application.

Books

  • 1 Higher Engineering Mathematics, Dr. B. S. Grewal, Khanna Publication.
  • 2 Advanced Engineering Mathematics, Erwin Kreyszig, Wiley Eastern Limited.
  • 3 Advanced Engineering Mathematics, R. K. Jain and S. R. K. Iyengar, Narosa publication
  • 4 Probability, Statistics and Random Processes, T. Veerarajan, Mc. Graw Hill education.
  • 5 Number theory, M. G. Nadkarni and J. S. Dani, Tata Mc. Graw Hill education.

Online References

  • 1 https://nptel.ac.in/courses/111/104/111104085/
  • 2 https://nptel.ac.in/courses/111/106/111106139/
  • 3 https://www.youtube.com/watch?v=2CP3m3EgL1Q
  • 4 https://www.youtube.com/watch?v=Hw8KHNgRaOE
  • 5 https://nptel.ac.in/courses/111/105/111105041/

Reproduced from the University of Mumbai syllabus for B.E. (Artificial Intelligence and Data Science), item 6.20 (N), under NEP 2020, in force from the academic year 2025-26. Wording, module numbering and hours are as printed in that syllabus.

The complete syllabus

This subject is cut from the University circular for its year. Open a document here if you want the whole thing rather than a single subject.

PDF B.E. Artificial Intelligence and Data Science - First Year, Semester I and II - NEP 2020 - Item 7.7 (R-A) NEP 2020, Semesters I and II, in force from 2024-25 Read full PDF Read
PDF B.E. Artificial Intelligence and Data Science - Second Year, Semester III and IV - NEP 2020 - Item 6.20 (N) NEP 2020, Semesters III and IV, in force from 2025-26 Read full PDF Read
PDF B.E. Artificial Intelligence and Data Science - Third Year, Semester V and VI - CBCS REV-2019 C Scheme - Item 6.42 (R) CBCS REV-2019 'C' Scheme, Semesters V and VI, in force from 2022-23 Read full PDF Read
PDF B.E. Artificial Intelligence and Data Science - Fourth Year, Semester VII and VIII - CBCS REV-2019 C Scheme - Item 6.12 (N) CBCS REV-2019 'C' Scheme, Semesters VII and VIII, in force from 2023-24 Read full PDF Read
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