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Government College Karauli
Government College Karauli
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| DEPARTMENT OF MATHEMATICS | |||
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| VIDEO - LECTURES BY RAFIQUE AHEMAD, ASSOCIATE PROFESSOR | |||
| YouTube Channel Link: | ||||
| Sr. No. | Video Name | Class | Topic | Video Link |
| 09 | 2D - Lecture -06 | B.Sc. Part I | Concept and definition of Parabola and a Conic. | https://youtu.be/tK3OqBItuws |
| 89 | Linear Algebra Lecture -34 | B.Sc. Part III | Existence Theorem : Every Finite Dimensional Vector Space has atleast one Basis. SHOW MORE | https://youtu.be/_fPf4pl5COQ |
| 88 | 2D - Lecture -05 | B.Sc. Part I | Circle : Condition of Tangency, Tangent of Given Slope, Chord of Contact and Pair of Tangents. | https://youtu.be/24WhmXZHUDA |
| 87 | Linear Algebra Lecture -33 | B.Sc. Part III | Generating Set, Finite Dimensional vector Space, basis of a vector Space. | https://youtu.be/D4KyJ_284y8 |
| 86 | 2D - Lecture -04 | B.Sc. Part I | Concept, Definition and Equations of a Circle. | https://youtu.be/XoRmzlStTBE |
| 85 | 2D - Lecture -03 | B.Sc. Part I | Straight Line and Pair of Straight Lines. | https://youtu.be/51peU0lCvIk |
| 84 | Real Analysis Lecture -36 | B.Sc. Part II | Concept and Definition of Supremum, Infimum, Limit Point and Limit of a Sequence. | https://youtu.be/Vv0QXt_moTI |
| 83 | Real Analysis Lecture -35 | B.Sc. Part II | Types of Real Sequence. | https://youtu.be/jGT4dFj1i6o |
| 82 | Real Analysis Lecture -34 | B.Sc. Part II | Concept and definition of Sequence and Real Sequence. Reperesentation of a sequence. | https://youtu.be/RskJgrb57y8 |
| 81 | 2D - Lecture -02 | B.Sc. Part I | Different equations of straight lines in 2D (Revision) | https://youtu.be/wSFNhTW8kFo |
| 80 | 2D - Lecture -01 | B.Sc. Part I | Introduction to B.Sc. Part I Introduction to syllabus and paper pattern Introduction to 2 Dimensional Geometry | https://youtu.be/1ARj9H57JYE |
| 79 | Linear Algebra Lecture -32 | B.Sc. Part III | Some more examples of LI & LD vectors. | https://youtu.be/puVgBd8vO84 |
| 78 | Linear Algebra Lecture -31 | B.Sc. Part III | Some more examples of LI & LD vectors. | https://youtu.be/MjwT34XyleE |
| 77 | Linear Algebra Lecture -30 | B.Sc. Part III | Some examples of LI and LD vectors. | https://youtu.be/gDEBXOP5lSQ |
| 76 | Linear Algebra Lecture -29 | B.Sc. Part III | Necessary and sufficient condition for some non-zero vectors to be LD. | https://youtu.be/rV_kfkzSy2c |
| 75 | Real Analysis Lecture -33 | B.Sc. Part II | Example : The set NXN is countable. | https://youtu.be/mwerWdPZWvQ |
| 74 | Real Analysis Lecture -32 | B.Sc. Part II | Example : The set Q of all rational numbers is countable. | https://youtu.be/6CqcrCI3Y8Q |
| 73 | Real Analysis Lecture -31 | B.Sc. Part II | Examples : Z and W are countable sets. | https://youtu.be/QPrQ5eaXTmI |
| 72 | Real Analysis Lecture -30 | B.Sc. Part II | Remaining part of the theorem : Union of two countable sets is countable. | https://youtu.be/FNbPyk8ICjI |
| 71 | Real Analysis Lecture -29 | B.Sc. Part II | Theorem : Union of two countable sets is countable (part I ) | https://youtu.be/8lhXcfyW2-I |
| 70 | Linear Algebra Lecture -28 | B.Sc. Part III | Theorem on Linearly Dependent Set | https://youtu.be/MLG-qTjUOWw |
| 69 | Linear Algebra Lecture -27 | B.Sc. Part III | Theorems on LI & LD vectors | https://youtu.be/UPPXC6nfogI |
| 68 | Linear Algebra Lecture -26 | B.Sc. Part III | Linearly Independent & Linearly Dependent Vectors. | |
| 67 | Real Analysis Lecture -28 | B.Sc. Part II | Theorem : Subset of a countable set is countable. | |
| 66 | Real Analysis Lecture -27 | B.Sc. Part II | Equivalent sets and Coutable Set. | |
| 65 | Linear Algebra Lecture -25 | B.Sc. Part III | Examples of linear combinations and linear span. | |
| 64 | Special Lecture -05 | B.Sc. Part III | Simlex Method - 01 : Flow Chart, Five Main Steps, Standard Form. | |
| 63 | Special Lecture -04 | B.Sc. Part III | Linear equation system and basic feasible solution (BFS) - Base of simplex method. | |
| 62 | Linear Algebra Lecture -24 | B.Sc. Part III | Theorem and example on linear span and linear combination. | |
| 61 | Real Analysis Lecture -26 | B.Sc. Part II | Examples : Union of infinite collection of closed sets may not be closed and Intersection of infinite collection of open sets may not be open. | |
| 60 | Real Analysis Lecture -25 | B.Sc. Part II | Union of finite collection of cloded sets is closed. | |
| 59 | Linear Algebra Lecture -23 | B.Sc. Part III | Some theorems on linear span. | |
| 58 | Linear Algebra Lecture -22 | B.Sc. Part III | Theorem : If S and T are non-empty subsets of a vector space then L(SUT) = L(S) + L(T) | |
| 57 | Special Lecture -03 | B.Sc. Part III | Relation between dimensions of vector space and subspaces, minimum number in generating set, minimum number in LI set. | |
| 56 | Real Analysis Lecture -24 | B.Sc. Part II | Intersection of finite collection of open sets is open. | |
| 55 | Real Analysis Lecture -23 | B.Sc. Part II | Intersection of arbitrary collection of closed sets is closed. | |
| 54 | Real Analysis Lecture -22 | B.Sc. Part II | Union of arbitrary collection of open sets is open. | |
| 53 | Special Lecture -02(b) | B.Sc. Part III | Revision of Generating set, Basis, Dimension, Existence Theorem, Extension Theorem etc. | |
| 52 | Special Lecture -02(a) | B.Sc. Part III | Revision of Vector Scace, Subspace, Linear Combination, Linear Span, LI & LD vectors, etc. | |
| 51 | Special Lecture -01 | B.Sc. Part III | For ( Session 2019-20) stutents who are goimg to apear in exams next week. | |
| 50 | Linear Algebra Lecture -21 | B.Sc. Part III | Linear span of union of two subspaces of a vector space is equal to the linear sum of that subspaces | |
| 49 | Linear Algebra Lecture -20 | B.Sc. Part III | Concept of Linear Sum & Theorem : Linear sum of two subspaces is a subspace | |
| 48 | Linear Algebra Lecture -19 | B.Sc. Part III | Linear span of a set S is the smallest subspace containing S. | |
| 47 | Linear Algebra Lecture -18 | B.Sc. Part III | Linear Combination & Linear Span. | |
| 46 | Linear Algebra Lecture -17 | B.Sc. Part III | Union of 2 subspaces is subspace if and only if one subspace is contained in other. | |
| 45 | Linear Algebra Lecture -16 | B.Sc. Part III | Intersection of two subspaces is always a subspace. But union may or may not be a subspace. | |
| 44 | Real Analysis Lecture -21 | B.Sc. Part II | R and void(empty) set are open sets as well as closed sets. | |
| 43 | Real Analysis Lecture -20 | B.Sc. Part II | Complement of open set is closed and complement of closed set is open. | |
| 42 | Real Analysis Lecture -19(b) | B.Sc. Part II | Finite set, N and Z are closed sets but they are not open sets. | |
| 41 | Real Analysis Lecture -19(a) | B.Sc. Part II | The set of all rational numbers Q is not open and is not closed. | |
| 40 | Linear Algebra Lecture -15 | B.Sc. Part III | More examples of subspaces. | |
| 39 | Real Analysis Lecture -18 | B.Sc. Part II | An open interval is not a closed set. and a closed interval is not an open set. | |
| 38 | Real Analysis Lecture -17 | B.Sc. Part II | An open interval is open set and closed interval is closed set. | |
| 37 | Linear Algebra Lecture -14 | B.Sc. Part III | More Examples of Subspaces | |
| 36 | Linear Algebra Lecture -13 | B.Sc. Part III | Some more examples of subspaces. | |
| 35 | Real Analysis Lecture -16 | B.Sc. Part II | Concept & Definition of Interior Point, Closed Set and Open Set. | |
| 34 | Real Analysis Lecture -15 | B.Sc. Part II | Concept and definition of isolated point, derived set and closure of a set | |
| 33 | Real Analysis Lecture -14(b) | B.Sc. Part II | Balzano-Weierstrass theorem on sets | |
| 32 | Real Analysis Lecture -14(a) | B.Sc. Part II | Concept of boundness and limit point of a set | |
| 31 | Real Analysis Lecture -13 | B.Sc. Part II | Concept and definition of limit point in real analysis | |
| 30 | Real Analysis Lecture -12 | B.Sc. Part II | Neighbourhood of a real number and deleted neighbourhood. | |
| 29 | Linear Algebra Lecture -12 | B.Sc. Part III | Examples of Subspaces | |
| 28 | Linear Algebra Lecture -11 | B.Sc. Part III | Necessary & sufficient condition for a non-empty subset of a vector space to be subspace in form of linear combination of two vectors. | |
| 27 | Linear Algebra Lecture -10 | B.Sc. Part III | Necessary & Sufficient Conditions for a non-void subset of a vector space to be a subspace. | |
| 26 | Real Analysis Lecture -11 | B.Sc. Part II | Irrational Density Theorem | |
| 25 | Real Analysis Lecture -10 | B.Sc. Part II | Rational Density Theorem | |
| 24 | Real Analysis Lecture -09 | B.Sc. Part II | Corollary of Archimedean property and Betweenness Theorem | |
| 23 | Linear Algebra Lecture -09 | B.Sc. Part III | Concept of vector subspace and some examples | |
| 22 | Linear Algebra Lecture -08(b) | B.Sc. Part III | Some more examples of Vector Space as Assignment/Home Work | |
| 21 | Linear Algebra Lecture -08(a) | B.Sc. Part III | Some examples of Vector Space as Assignment/Home Work | |
| 20 | Real Analysis Lecture -08 | B.Sc. Part II | Archimedean property and Archimedean field | |
| 19 | Linear Algebra Lecture -07(b) | B.Sc. Part III | Properties of vector spaces | |
| 18 | Linear Algebra Lecture -07(a) | B.Sc. Part III | Some properties of vector spaces | |
| 17 | Linear Algebra Lecture -06 | B.Sc. Part III | Two Examples of Vector Spaces | |
| 16 | Real Analysis Lecture -07(b) | B.Sc. Part II | Ordered field Q of all rational numbers is not a complete ordered field | |
| 15 | Real Analysis Lecture -07(a) | B.Sc. Part II | Concept of Completeness by Supremum & Infimum Axioms and by Dedekind's Axioms. | |
| 14 | Linear Algebra Lecture -05 | B.Sc. Part III | An example of vector space of polynomials | |
| 13 | Real Analysis Lecture -06(b) | B.Sc. Part II | Supremum and Infimum | |
| 12 | Real Analysis Lecture -06(a) | B.Sc. Part II | Upper Bound, Lower Bound, Supremum and Infimum of a subset of an Ordered Field. | |
| 11 | Linear Algebra Lecture -04 | B.Sc. Part III | An example of a vector space of functions | |
| 10 | Real Analysis Lecture -05 | B.Sc. Part II | Real Number Line , Intervals and Absolute Value of a Real Number | |
| 9 | Linear Algebra Lecture -03 | B.Sc. Part III | Example of vector space of matrices | |
| 8 | Real Analysis Lecture -04 | B.Sc. Part II | Ordered Field is infinite field. squre root of 2 is irrational | |
| 7 | Linear Algebra Lecture -02 | B.Sc. Part III | Definition & Example of Vector Space | |
| 6 | Real Analysis Lecture -03 | B.Sc. Part II | Properties of Ordered Field | |
| 5 | Real Analysis Lecture -02 (Again) | B.Sc. Part II | Ordered Field | |
| 4 | Linear Algebra Lecture -01 | B.Sc. Part III | Revision of field and introduction to definition of vector space. | |
| 3 | Real Analysis Lecture -02 | B.Sc. Part II | Ordered Field | |
| 2 | Real Analysis Lecture -01 | B.Sc. Part II | Basics of Ordered Field | |
| 1 | Group Morphism 1 | B.Sc. Part I | Group Morphism | |
