IIT Madras Maths 1 Lectures: Mathematics for Data Science I
BSMA1001189 lectures12 weeks
Weeks
- Week 116 lecturesMathematics for Data Science 1 | introduction to the course basics · Natural numbers & their operations - fundamentals for data science · Rational numbers - fractions & their properties explained · Real & complex numbers - understanding rational & irrational numbers · Set theory - introduction to sets & their operations · Construction of subsets & set operations - set comprehension &intervals explained · Sets examples - membership subsets & set comprehension with practice · Examples of set operations & counting problems - venn diagrams & applications · Relations - cartesian products equivalence & partitioning sets · Functions - domain codomain range & properties of mappings · Relations examples - cartesian products tables & join operations · Function examples - domains ranges & growth of functions · Prime numbers - euclids proof infinitude & applications in cryptography · Why is a number irrational - proof of sqrt2 & the story of hippasus · Sets versus collections - russells paradox & mathematical foundations · Degrees of infinity - countable & uncountable sets explained
- Week 226 lecturesRectangular coordinate system - axes points lines & quadrants · Distance formula - calculating distance between two points in coordinate geometry · Section formula - dividing a line segment in a given ratio · Area of a triangle - formula derivation using coordinates · Slope of a line - rise over run & angle of inclination · Parallel & perpendicular lines - slope conditions & angle of intersection · Representation of a line 1 - point slope & two point forms explained · Representation of a line 2 - slope intercept & intercept forms · Rectangular Co-ordinate system and its elementary applications · General equation of a line - forms conversions & geometric properties · Equation of parallel & perpendicular lines in general form · Equation of a perpendicular line through a point using slope conditions · Distance of a point from a line - perpendicular distance & parallel lines · Straight line fit - vertical distance sum of squared errors & regression · Tutorial 1 · Tutorial 2 · Tutorial 3 · Tutorial 4 · Tutorial 5 · Tutorial 6 · Tutorial 7 · Tutorial 8 · Tutorial 9 · Additional Lecture 01 · Additional Lecture 02 · Additional Lecture 03
- Week 317 lecturesSummary lecture · Solution of a quadratic equation using factorization · Solution of a quadratic equation using square method · Quadratic formula | completing the square, discriminant & nature of roots · Summary · Tutorial 1 · Tutorial 2 · Tutorial 3 · Tutorial 4 · Tutorial 5 · Tutorial 6 · Tutorial 7 · Tutorial 8 · Tutorial 9 - point of intersection of two lines · Part B: Surface of revolution | cone formation by rotating a line · Part A: Additional lecture | standard form & vertex form of parabola · Additional Lecture - 3.1
- Week 426 lecturesIntroduction to polynomials definition & types · Quadratic functions - graphs vertex & parabolas · Examples of quadratic functions · Slope of a quadratic function · Solution of a quadratic equation using graph · Degree of polynomials definition examples & special cases · Slope line & parabola · Algebra of polynomials addition & subtraction explained with examples · Algebra of polynomials multiplication methods & examples · Algebra of polynomials division with remainders explained · Polynomial division algorithm with long division explained · Graphs of polynomials identification & characterization explained · Zeroes of Polynomial Functions · Graphs of polynomials behavior at x intercepts & multiplicities · Graphs of Polynomials: Multiplicities · Graphs of polynomials end behavior leading term & degree explained · Graphs of polynomials turning points & relation to degree · Graphs of polynomials graphing methods & polynomial creation · Tutorial 1 · Tutorial 2 · Tutorial 3 · Tutorial 4 · Tutorial 5 · Tutorial 6 · Tutorial 7 · Tutorial 8
- Week 516 lecturesOne-to-one function definition, tests & exponential basics · One-to-one function examples, cubic cases & theorems · Exponential functions definition & properties · Exponential functions graphing with examples & analysis · Natural exponential function definition properties & applications · Composite functions definition domain & real world examples · Composite functions step by step examples & practice · Composite functions finding the domain with examples · Inverse functions definition & graphical symmetry · Tutorial 1 · Tutorial 2 · Tutorial 3 · Tutorial 4 · Tutorial 5 · Tutorial 6 · Tutorial 7
- Week 619 lecturesLogarithmic functions & inverse of exponential functions · Graphs & properties of logarithmic functions · Solving exponential equations with logarithms · Logarithmic functions – properties & fundamental laws · Logarithmic functions – applications of log laws · Logarithmic functions – change of base theorem · Logarithmic equations – solving & applications · Tutorial 1 · Tutorial 2 · Tutorial 3 · Tutorial 4 · Tutorial 5 · Tutorial 6 · Tutorial 7 · Tutorial 8 · Additional Lecture supplementary concepts in mathematics for data science · Weekly summary: polynomial definitions & algebra operations · Practice Assignment Solution · PA solution
- Week 712 lecturesTutorial 1 · Tutorial 2 · Tutorial 3 · Tutorial 4 · Tutorial 5 · Tutorial 6 · Tutorial 7 · Tutorial 8 · Tutorial 9 · Summary: polynomial graphs & real-world applications · Practice Assignment Solution · PA Solution
- Week 811 lecturesGraphing basic functions & their properties · Graphing quadratic functions using roots & vertex · Graphing cubic polynomial functions in intercept form · Range of square root functions with restricted domain · Range of square root functions with restricted domain · Domain of composite functions with examples · Optimization with birthday & sunday discount problem · Compound interest & inverse function in financial math · Additional lecture: inverse functions finding & verifying with examples · PRACTICE ASSIGNMENT SOLUTION · PA Solution
- Week 98 lecturesSolving logarithmic equations with multiple bases · Solving logarithmic equation with integer solutions · Activation energy estimation using sum of squared errors & arrhenius equation · Categorizing points using sigmoidal function (G1 & G2 classification) · Solving logarithmic function intersection problem · Solving logarithmic equations with exponents & substitution · Practice Assignment Solution · PA Solution
- Week 1013 lecturesIntroduction to graphs – vertices, edges & connectivity · Some general graph problems · Representation of graphs · Breadth-first search · Depth-first search (DFS) · Applications of BFS & DFS | part 1 · Applications of BFS & DFS | part 2 · Complexity of BFS & DFS · Directed Acyclic Graphs · Topological sorting · Tutorial 1 · Tutorial 2 · Tutorial 3
- Week 1110 lecturesLongest paths in DAGs – task scheduling & dependencies · Transitive closure | reachability in graphs · Matrix multiplication | graphs, boolean algebra & transitive closure · Shortest paths in weighted graphs | single source & all pairs · Single source shortest paths | dijkstra’s algorithm · Single source shortest paths with negative weights | bellman-ford algorithm · All-pairs shortest paths | floyd-warshall algorithm · Minimum cost spanning trees | prim’s & kruskal’s algorithms · Minimum cost spanning trees | prim’s algorithm · Minimum cost spanning trees | kruskal’s algorithm
- Week 127 lecturesRevision lecture on set theory | venn diagrams, operations & python applications · Revision lecture on relations | properties, representations & applications · Revision lecture on polynomial graphing | roots, turning points & visualizations · Revision lecture on functions | basics, domain & range · Revision lecture on logarithmic functions · Revision lecture on basics of graph theory · Revision lecture on exponential & composite function
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