Workshop on Foundations of Mathematics - Remedial Coaching Cell
Dear Students,
As part of the Remedial Coaching Cell, we are organizing a series of lectures on the Foundations of Mathematics by eminent mathematician Prof. S. Kumaresan, Programme Director of Mathematics Training and Talent Search (MTTS). MTTS is the most popular undergraduate training camp of this country MTTS. To know more about the programme please visit https://mtts.org.in.
To register for this course, please enroll yourself for the course titled "Workshop on Foundations of Mathematics - Remedial Coaching Cell" at courses.cutn.ac.in with the password "RCC_CUTN".
Eligibility: Any student of the Integrated MSc programme of the Department of Mathematics.
The lectures will be online mode. More details will be communicated to the registered participants.
Register as early as possible.
Best regards,
Chandrashekaran
Partial Differential Equations 2022
The objective of the course is to enable the students to understand the theory of partial differential equations arising in various fields of sciences. Topics include the method of characteristics, classification of second-order PDEs, canonical forms, hyperbolic, parabolic, and elliptic differential equations.
Scientific Computing Lab - II 2022
Subject Code: MAT222
Credits: 2
Scientific Computing Lab II
ReviewofPythoncommands,Pythonvariables,SymbolicVariables,Firstcom- putations; Elementary functions and Usual constants; Auto completion; Sim- ple plotting.
SymbolicExpressionsandSimplification;Transformingexpressions;UsualMath- ematical functions; Assumptions and pitfalls; Explicit solving of Equations; Equa- tion with no explicit solution; Sums; Limits; Sequences; Power Series Expan- sions; Series; Derivaties; Partial Derivatives; Integrals; Solving linear systems; Vector Computations; Matrix Computations; Reduction of a Square Matrix
Programming with Sage; Python language keywords; Sage Keywords; Special symbols in Sage and their uses; Function Calls; Algorithms - Loops; Approxi- mation of Sequence Limits; Conditionals; Procedures and functions; Iterative and recursive methods; Input and Output
Lists and Othere Data Structures; List creation and access; Global list opera- tions; Main methods on lists; Examples of list manipulations; Character Strings; Shared or Duplicated Data Structures; Mutable and Immutable Data Structures; Finite sets; Dictionaries;
2DGraphics-Graphicalrepresentationofafunction;ParametricCurve;Curves in Polar Coordinateds; Curve Defined by an implicit function; Data Plot; Dis- playing solutions of differential equations; Evolute of a curve; 3D Graphics
StatisticswithSagemath:Basicfunctions-random,mean,median,mode,mov-
ing average, std, variance; C Int Stats - stats.IntList, min, max, plot, histogram, product, sum; Distributions - norm, uniform, expon, bernoulli, poisson; Statis-
tical functions - stats.gmean, stats.hmean, stats.skew, stats.histogram2, stats.kurtosis, stats.linregress; Statistical model - linear fit - stats.glm
References.
P. Zimmermann et.al., Mathematical Computation with Sage, SIAM, Philadel- phia, 2018. (http://sagebook.gforge.inria.fr/english.html)
R.A.Mezei,AnIntroductiontoSAGEProgramming:WithApplicationstoSAGE Interacts for Numerical Methods, John Wiley & Sons, 2015.
G.A.Anastassiou,R.A.Mezei,NumericalAnalysisUsingSage,Springer,2015.
R.A.Beezer,AFirstCourseinLinearAlgebra,UniversityPressofFlorida,2009.
A.Kumar&S.G.Lee,LinearAlgebrawithSage,KyoboBooks,2015. (http://matrix.skku.ac.kr/2015-Album/Big-Book-LinearAlgebra-Eng-2015.pdf )
https://docs.scipy.org/doc/scipy/reference/stats.html
Probability and Statistics 2022
Semester IV Subject Code: MAT221
Credits: 4
Probability and Statistics
Probability, Random experiment; Sample point, Event and Probability; Rules of Probability; Conditional Probability; Independence of Events; Bayes’ Rule. Applications.
Discrete Random variables Definition; sum and linear composite of random variables; Mean and variance; Bernoulli, Binomial, geometric and negative bi- nomial distributions; hypergeometric distribution; Poisson distribution. Ap- plications.
Continuous Random Variables. Definition; Uniform and exponential distribu- tions; Normal distribution and its properties; Standard normal distribution; Transformation from a general normal distribution to standard normal; Check- ing for normality of data; Applications.
Point Estimation and Confidence Intervals Point estimation of the population mean and standard deviation of a normal distribution; Estimation of propor- tion; Confidence intervals; Large sample methods; Applications.
Hypothesis Testing Hypothesis - simple and composite; Null and alternative; Test of Hypothesis; Type I and Type II errors; Level and power of a test; p-value; Tests for mean and standard deviation; Test for proportion; one tail or two tails. Applications.
References
A.D. Aczel, and J. Sounderpandian Complete Business Statistics, 7th Edition, McGraw-Hill, Irwin, 2008.
S.C. Gupta, V.K. Kapoor, Fundamentals of Mathematical Statistics (A Modern Approach), 10th Edition, Sultan Chand and Sons, 2000.
M.L.Samuels,andJ.A.Witmer,Statisticsforthelifesciences,3rdEdition,Pren- tice Hall, 2003.
H.E.VanEmden,StatisticsforterrifiedBiologists,BlackwellPublishing,2008.
R. Barlow, Statistics - A guide to the use of statistical methods in the Physical Sciences, Wiley, 1999.