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MTH100 : General Mathematics

Course Overview

Course Synopsis

This course contents are: Sets, Real Numbers , Complex Numbers, Functions, Quadratic Functions, Matrices, Inverse of a Matrix, Determinants, Arithmetic Progression and Arithmetic Series, Geometric progression and Geometric Series, Permutations and Combinations, Binomial theorem, Graphs and Functions, Straight Lines and Circles, Trigonometry, Statistics Introduction, Introduction to data, Frequency Distributions, Graphical representation of data, Measures Of Central Tendency, Range, inter quartile deviation mean deviation, Moments, Skewness and kurtosis.

Course Learning Outcomes

By the end of the course, students should be able to learn:

  • Define sets, representation of sets, operations on sets.
  • Natural Numbers, Integers, Rational Numbers, Irrational Numbers, Real Numbers. Properties of Real Numbers
  • Need for complex numbers, definition of complex numbers, properties of complex numbers
  • Definition of a function, types of functions, domain and range of a function, composition of functions, inverse functions
  • Solution of quadratic equations, completing the square and quadratic formula, nature of the roots, equations reducible to quadratic equations
  • Definition of a matrix, types of matrices, operations on matrices,Inverses, solving systems of equations using inverses,Definition of determinants, cofactors, evaluation of second and third order determinants, properties of determinants, Cramer’s Rule
  • sequences. Arithmetic sequences, common difference and nth term. Sum of an arithmetic series. Applications, Geometric sequences, common ratio and nth term. Finite sum of a geometric series. Sum of an infinite geometric series. Applications
  • Factorial notation. Permutations. Combinations. Applications.
  • Binomial forms. Binomial theorem and the binomial formula.
  • Basic concepts. Cartesian Coordinates. Use of symmetry, Distance formula ,Equation of a straight line, slopes and intercepts. Graphs of straight lines. Equation of a circle.,
  • Radians and Degrees. Basic trigonometric functions – sine, cosine, tangent, secant, cosecant and cotangent - and their graphs. Inverse trigonometric functions. Solving trigonometric equations. Addition formulas. Double Angle formulas, trigonometric identities.Addition formulas. Double Angle formulas, trigonometric identities.
  • Definition of statistics. Descriptive and Inferential statistics. Population and Sample. Limitations of statistics, Meaning of data. Types of data. Summation notation. Quantitative and qualitative data. Discrete and Continuous data. Types of intervals, Types of frequency distributions. Class intervals, class boundaries, class midpoints, frequencies, relative frequencies, Bar charts, histograms, frequency polygons, cumulative frequency polygon. Symmetry and skewness. Percentile, deciles and quartiles


Course Calendar

TopicLectureResourcePage
Sets and Numbering Systems1Handouts1-5
Sets and Numbering Systems2Handouts1-5
Sets and Numbering Systems3Handouts1-5
Function and Quadratics4Handouts6-12
Function and Quadratics5Handouts6-12
Function and Quadratics6Handouts6-12
Function and Quadratics7Handouts6-12
Quiz # 1 (Lecture 1 to Lecture 7)
Matrices and Determinants8Handouts13-21
Matrices and Determinants9Handouts13-21
Matrices and Determinants10Handouts13-21
Matrices and Determinants11Handouts13-21
Matrices and Determinants12Handouts13-21
Sequence and Series13Handouts22-23
Sequence and Series14Handouts22-23
Assignment # 1 (From Lec 8 to Lec 14)
Sequence and Series15Handouts22-23
Review of Sets16Handouts1-5
Review of Functions17Handouts6-12
Review of Matrices18Handouts13-21
Permutations19Handouts24-25
Combinations20Handouts24-25
Assignment # 2 (From lec 15 to lec 20)
Binomial theorem21Handouts26-27
Coordinate Geometry22Handouts28-30
Mid Term Examination
Coordinate Geometry23Handouts28-30
Coordinate Geometry and Trigonometry24Handouts28-30
Trigonometry25Handouts31-42
Trigonometry26Handouts31-42
Trigonometry27Handouts31-42
Trigonometry28Handouts31-42
Trigonometry29Handouts31-42
Trigonometry30Handouts31-42
Quiz # 2 (Lecture 23 to Lecture 30)
Review of Sequence and Series31Handouts22-23
Review of Permutation and Combination, Binomial Theorem32Handouts24-25
Review of Binomial Theorem, Coordinate Geometry33Handouts26-27
Assignment # 3 (From Lec 22 to Lec 33)
Review of Coordinate Geometry, Trigonometry34Handouts28-30
Statistics35Handouts43-46
Statistics36Handouts43-46
Representation of Data37Handouts47-51
Measures of Central Tendency38Handouts52-55
Measures of Central Tendency39Handouts52-55
Measures of Central Tendency and Measures of Dispersion40Handouts56-62
Measures of Dispersion41Handouts56-62
Measures of Dispersion42Handouts56-62
Skewness and Kurtosis43Handouts63-67
Skewness and Kurtosis44Handouts63-67
Probability Concepts45Handouts68-69
Final Examination
 
 
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