39.45 GB | 35min 14s | mp4 | 1280X720 | 16:9
Genre:eLearning |Language:English
Files Included :
1 Introduction to the course.mp4 (69.54 MB)
1 Plenty of symbols to get acquainted with.mp4 (20.48 MB)
2 Greek letters in mathematics.mp4 (326.82 MB)
3 Latin letters in mathematics.mp4 (225.73 MB)
1 Quite informally about the need for introducing new number types, from N to C.mp4 (353.07 MB)
10 Rational numbers as fractions.mp4 (253.31 MB)
11 Decimal expansion of rational numbers.mp4 (54.76 MB)
12 Finite and periodic decimal expansions.mp4 (131.39 MB)
13 Finite and periodic decimal expansions, Problem 3.mp4 (87.89 MB)
14 Finite and periodic decimal expansions, Problem 4.mp4 (83.02 MB)
15 Finite and periodic decimal expansions, Problem 5.mp4 (195.68 MB)
16 The mysterious irrational numbers.mp4 (223.71 MB)
17 The distributive law, Problem 6.mp4 (159.63 MB)
18 Arithmetic, Problem 7.mp4 (156.38 MB)
19 The distributive law, Problem 8.mp4 (80.17 MB)
2 Natural numbers arithmetic; multiplication has higher precedence than addition.mp4 (229.76 MB)
20 Order of operations (precedence rules), Problem 9.mp4 (341.01 MB)
21 The distributive law and precedence rules don't contradict each other.mp4 (236.19 MB)
22 Arithmetic, Problem 10.mp4 (251.06 MB)
23 Arithmetic, Problem 11.mp4 (189.18 MB)
24 Arithmetic, Problem 12.mp4 (197.31 MB)
25 Future Domain of a function of two variables, Problem 13.mp4 (279.81 MB)
26 Future Values of a function of two variables, Problem 14.mp4 (152.03 MB)
27 Arithmetic, Problem 15.mp4 (410.52 MB)
28 Future the derivative of a polynomial, Problem 16.mp4 (157.13 MB)
3 Commutativity of addition and multiplication.mp4 (66.39 MB)
4 Associativity of addition and multiplication.mp4 (35.55 MB)
5 The distributive law and its consequences.mp4 (204.83 MB)
6 Prime numbers and some divisibility rules.mp4 (29.68 MB)
7 Prime factorization, Problem 1.mp4 (216.44 MB)
8 How to find prime numbers Problem 2.mp4 (239.98 MB)
9 Integer numbers addition, subtraction, and multiplication.mp4 (112.84 MB)
1 Distance is necessary for Calculus.mp4 (34.45 MB)
10 Advanced Unit circles can be strange in Taxi cab metric.mp4 (64.94 MB)
11 Advanced Unit circles can be strange in max metric.mp4 (28.04 MB)
12 Future Why is distance necessary for Calculus.mp4 (54.24 MB)
2 Distance between real numbers; absolute value.mp4 (245.14 MB)
3 Cartesian coordinate system in R2, reflections about axes.mp4 (123.46 MB)
4 Pythagorean Theorem and Euclidean distance between points in the plane.mp4 (201.46 MB)
5 What is triangle inequality and why is it essential for Calculus.mp4 (49 MB)
6 Advanced Distances in metric spaces.mp4 (572.98 MB)
7 Advanced Taxi cab distance Manhattan distance.mp4 (372.42 MB)
8 Advanced Max distance in the plane.mp4 (65.48 MB)
9 Advanced Open ball and deleted (punctured) neighbourhood.mp4 (71.79 MB)
1 Equations unknowns, solutions (roots), solution sets.mp4 (49.65 MB)
10 Linear equations with absolute value, Problem 4.mp4 (73.34 MB)
11 Linear equations with absolute value, Problem 5.mp4 (73.7 MB)
12 Linear equations with absolute value, Problem 6.mp4 (105.94 MB)
13 Future Examples of equations and their solution sets.mp4 (54.33 MB)
14 Equations of straight lines in the plane slope and intercept.mp4 (103.72 MB)
15 Equations of straight lines in the plane, Problem 7.mp4 (240.25 MB)
16 Operations which do not change the solution set of an inequality.mp4 (46.76 MB)
17 Careful with multiplying inequalities by variable expressions.mp4 (39.04 MB)
18 Linear inequalities, Problem 8.mp4 (115.32 MB)
19 How to handle inequalities with absolute value.mp4 (68.47 MB)
2 Inequalities variables, solution sets.mp4 (260.6 MB)
20 Linear inequalities with absolute value, Problem 9.mp4 (221.79 MB)
21 Linear inequalities with absolute value, Problem 10.mp4 (173.76 MB)
22 Linear inequalities with absolute value, Problem 11.mp4 (276.4 MB)
23 Future Equations and inequalities in one variable, in Calculus 1 and 2.mp4 (57.94 MB)
24 Future Equations and inequalities in two variables, in Calculus 3.mp4 (46.72 MB)
25 Advanced A strange circle from Videos 39 and 42, Problem 12.mp4 (74.46 MB)
26 What about systems of linear equations.mp4 (104.45 MB)
3 What does it mean to solve an equation or inequality, to verify a solution.mp4 (190.15 MB)
4 Examples of equations with one unknown and where to find them.mp4 (30.42 MB)
5 Operations which do not change the solution set of an equation.mp4 (138.23 MB)
6 Inconsistent equations and false roots.mp4 (299.47 MB)
7 Linear equations, Problem 1.mp4 (205.52 MB)
8 Linear equations with absolute value, Problem 2.mp4 (557.13 MB)
9 Linear equations with absolute value, Problem 3.mp4 (240.93 MB)
1 Function as a relation between variables independent and dependent.mp4 (81.06 MB)
10 Various ways of describing functions 3 with a table.mp4 (36.65 MB)
11 Various ways of describing functions 4 with a verbal description.mp4 (167.64 MB)
12 Surjections, injections, bijections How to detect injections.mp4 (189.25 MB)
13 Inverse functions.mp4 (218.67 MB)
14 Monotone functions increasing, decreasing, non-decreasing, non-increasing.mp4 (51.4 MB)
15 Bounded functions bounded above and bounded below, maximum, minimum.mp4 (136.26 MB)
16 How to scale, add, subtract, multiply, and divide functions.mp4 (225.08 MB)
17 What is a composition of functions.mp4 (199.46 MB)
18 Future Why is the order of functions in a composition important.mp4 (143.44 MB)
19 Even and odd functions Future integration by inspection.mp4 (66.17 MB)
2 Function as a relation between variables; graph and vertical-line test.mp4 (166.22 MB)
20 Transformations of graphs.mp4 (439.64 MB)
21 Various operations on functions, Problem 1.mp4 (210.09 MB)
22 Inverse function, its domain and range, Problem 2.mp4 (385.83 MB)
23 Two similar functions with different domains, Problem 3.mp4 (149.64 MB)
24 Piecewise functions, Problem 4.mp4 (360.69 MB)
25 Piecewise functions, Problem 5.mp4 (303.45 MB)
26 Piecewise functions, Problem 6.mp4 (130.41 MB)
27 Functions with absolute value, Problem 7.mp4 (433.62 MB)
28 Transformations of graphs, Problem 8.mp4 (80.38 MB)
29 Transformations of graphs, Problem 9.mp4 (23.78 MB)
3 Function as a relation between variables; implicit versus explicit.mp4 (53.05 MB)
30 Heaviside step function, Problem 10.mp4 (42.28 MB)
31 Even and odd functions, Problem 11.mp4 (181.69 MB)
32 Domain and range of a composed function, Problem 12.mp4 (211.05 MB)
33 Advanced Domain and range, Problem 13.mp4 (40.96 MB)
34 Advanced A complicated function, Problem 14.mp4 (216.52 MB)
35 Advanced, Future The derivative of the function from V104, Problem 15.mp4 (152 MB)
36 Even and odd functions, Problem 16.mp4 (392.64 MB)
4 Examples of functions of one variable and where to find them.mp4 (57.96 MB)
5 How to think about sets, their unions, intersections, and differences.mp4 (93 MB)
6 Functions domain, codomain, range.mp4 (30.15 MB)
7 Various ways of describing functions 1 with a formula.mp4 (264.69 MB)
8 Determining the domain three typical issues to remember.mp4 (184.97 MB)
9 Various ways of describing functions 2 with a picture.mp4 (185.2 MB)
1 What is a statement and logical value; open and closed statements.mp4 (82.79 MB)
10 Equivalence versus equality.mp4 (22.49 MB)
11 Tautology as a logical formula.mp4 (113.07 MB)
12 How to verify tautologies.mp4 (122.1 MB)
13 Tautologies, Problem 1.mp4 (220.28 MB)
14 Tautologies, Problem 2.mp4 (171.55 MB)
15 Tautologies, Problem 3.mp4 (182.2 MB)
16 Tautologies, Problem 4.mp4 (102.79 MB)
17 Tautologies, Problem 5.mp4 (165.08 MB)
18 Advanced Tautologies, Problem 6.mp4 (182.85 MB)
19 Existential quantifier THERE EXISTS.mp4 (284.01 MB)
2 To be or not to be in the delta neighbourhood of some point.mp4 (41.02 MB)
20 Universal quantifier FOR ALL; Order matters; Precedence rules.mp4 (323.53 MB)
21 Negations De Morgan's Laws for quantifiers, Problem 7.mp4 (61.98 MB)
22 Logic, Problem 8.mp4 (274.83 MB)
23 Logic, Problem 9.mp4 (346.63 MB)
24 Logic, Problem 10.mp4 (132.49 MB)
25 Future, advanced Sequences, Problem 11.mp4 (279.96 MB)
26 Epsilon-delta, here we come!.mp4 (48.89 MB)
27 Advanced Negation L is not the limit.mp4 (78.21 MB)
3 Unary logical connective Negation NOT.mp4 (89.79 MB)
4 Binary logical connective 1 Conjunction AND.mp4 (221.5 MB)
5 Binary logical connective 2 Disjunction OR.mp4 (158.09 MB)
6 Connectives, Example 5.mp4 (171.44 MB)
7 Binary logical connective 3 Implication IF THEN A necessary condition.mp4 (53.39 MB)
8 Converse, inverse, and contrapositive statements.mp4 (83.85 MB)
9 Binary logical connective 4 Equivalence IFF A necessary and sufficient cond.mp4 (38.02 MB)
1 Primitive notions set, belonging to a set, the empty set.mp4 (66.48 MB)
10 Set difference.mp4 (18.67 MB)
11 Symmetric difference.mp4 (16.76 MB)
12 Complement defined with help of negation.mp4 (363.65 MB)
13 The laws of set theory and the laws of logic.mp4 (58.28 MB)
14 De Morgan's Laws, an illustration and proof.mp4 (193.46 MB)
15 The distributive law, an illustration and proof.mp4 (207.16 MB)
16 Set difference and symmetric difference, Problem 1.mp4 (232.35 MB)
17 Cartesian product of sets.mp4 (51.95 MB)
18 Power set of a given set; an example of Boolean algebra.mp4 (35.69 MB)
19 Cardinality of sets.mp4 (20.92 MB)
2 The universe and its subsets.mp4 (19.29 MB)
20 Cardinality of sets, Problem 2.mp4 (146.39 MB)
21 Optional Equinumerous (equipotent) sets; cardinal numbers.mp4 (34.73 MB)
22 Optional Finite, countable and uncountable sets.mp4 (27.45 MB)
23 Optional Comparing cardinalities of sets, Problem 3.mp4 (512.96 MB)
24 Optional Comparing cardinalities of sets, Problem 4.mp4 (94.14 MB)
25 Inclusion-exclusion principle.mp4 (57.16 MB)
26 Inclusion-exclusion principle, Problem 5.mp4 (207.11 MB)
27 Transposition law and subsets, Problem 6.mp4 (38.34 MB)
3 If you know logic, you know the set theory.mp4 (85.32 MB)
4 Intersection defined with help of conjunction.mp4 (156.44 MB)
5 Union defined with help of disjunction.mp4 (96.73 MB)
6 Equality of sets defined with help of equivalence Axiom of Extensionality.mp4 (29.13 MB)
7 Subset defined with help of implication.mp4 (22.1 MB)
8 The empty set gives a false statement.mp4 (16.56 MB)
9 The universe gives a true statement.mp4 (12.47 MB)
1 Relations in a regular sense.mp4 (44.54 MB)
10 Relation congruence modulo n.mp4 (92.09 MB)
11 Equivalence classes and partitions of a set.mp4 (222.99 MB)
12 More properties of relations irreflexive, antisymmetric, strongly connected.mp4 (205.2 MB)
13 Order relations.mp4 (66.79 MB)
14 Partial orders and Hasse diagrams.mp4 (70.88 MB)
15 Relations, Problem 6.mp4 (373.49 MB)
16 Relations, Problem 7.mp4 (272.04 MB)
17 Relations, Problem 8.mp4 (380.44 MB)
18 Relations, Problem 9.mp4 (147.64 MB)
2 Relations in a mathematical sense.mp4 (46.98 MB)
3 Relation a formal definition and notation.mp4 (52.07 MB)
4 How to plot relations.mp4 (53.21 MB)
5 How to plot relations, Problem 1.mp4 (48.16 MB)
6 Relations on finite sets, and their graphs, Problem 2.mp4 (208.93 MB)
7 RST relations equivalence relations.mp4 (289.43 MB)
8 How to recognize an RST relation from its plot.mp4 (54.7 MB)
9 How to recognize an RST relation on a finite set from the graph.mp4 (245.01 MB)
1 Some early signs.mp4 (45.27 MB)
10 Advanced A theorem about inverse function.mp4 (214.93 MB)
11 Advanced, future A really important theorem about compositions of functions.mp4 (386.5 MB)
2 Each function is a relation, not every relation is a function.mp4 (46.18 MB)
3 Each relation is invertible!.mp4 (65.88 MB)
4 Relations and functions, Problem 1.mp4 (144.71 MB)
5 Relations and functions, Problem 2.mp4 (119.82 MB)
6 Relations and functions, Problem 3.mp4 (268.3 MB)
7 Equality of functions, Problem 4.mp4 (37.67 MB)
8 Surjections and injections, Problem 5.mp4 (537.44 MB)
9 Future Cancellation law for injective functions and why it is important.mp4 (414.62 MB)
1 How we build mathematical theories.mp4 (35.23 MB)
10 Series of equivalences.mp4 (34.16 MB)
11 Proof by contradiction.mp4 (151.37 MB)
12 Existence, uniqueness, counter-examples.mp4 (317.71 MB)
13 Proof of the partition theorem from Video 171.mp4 (496.55 MB)
14 Construction of the natural numbers; Peano and induction.mp4 (425.04 MB)
15 Proof by induction, Problem 1.mp4 (261.78 MB)
16 Proof by induction, Problem 2.mp4 (403.8 MB)
17 Proof by strong induction, Problems 3 and 4.mp4 (634.14 MB)
18 Proof of three statements about natural numbers.mp4 (310 MB)
19 Prove or disprove.mp4 (563.64 MB)
2 Examples of primitive notions and definitions.mp4 (67.63 MB)
20 Define the set of integers using an equivalence relation and the set N.mp4 (264.29 MB)
21 Define the set of rational numbers using an equivalence relation and the set Z.mp4 (310.59 MB)
22 Some algebraic structures and where to find them.mp4 (62.41 MB)
23 Construction of the real numbers.mp4 (416.33 MB)
24 Some examples of proofs directly from the axioms.mp4 (385.72 MB)
25 The glorious and majestic Zero-Product Property.mp4 (166.51 MB)
26 The square root of 2 is irrational.mp4 (164.66 MB)
27 Density of Q and RQ in R.mp4 (121.84 MB)
28 A real number is irrational iff its decimal expansion is infinite aperiodic.mp4 (132.64 MB)
29 Optional Set of real numbers and set of irrational numbers are not countable.mp4 (76.34 MB)
3 Axioms.mp4 (87.7 MB)
30 The last piece of the epsilon-delta definition.mp4 (15.81 MB)
31 Future Proof that the limit of sum is equal to the sum of limits.mp4 (287.29 MB)
4 Theorems, propositions, lemmas, corollaries.mp4 (30.86 MB)
5 Types of proofs.mp4 (70.7 MB)
6 Direct proof (deduction and reduction).mp4 (430.23 MB)
7 Proof by cases.mp4 (215.76 MB)
8 Proof by contrapositive.mp4 (223.32 MB)
9 Proof of the extended version of the Cancellation law from Video 187.mp4 (367.66 MB)
1 The Sigma symbol, Problem 1.mp4 (222.43 MB)
10 Series as sums of the elements in a sequence.mp4 (67.84 MB)
11 Convergent and divergent series.mp4 (22.35 MB)
12 Arithmetic series, Problem 6.mp4 (245.22 MB)
13 Geometric series, Problem 7.mp4 (269.54 MB)
14 Harmonic series, Problem 8.mp4 (78.6 MB)
15 Limit of a sequence; Cauchy sequences.mp4 (100.46 MB)
16 Future Proof that the limit of a sum is equal to the sum of limits.mp4 (162.43 MB)
17 So, what's next.mp4 (55.49 MB)
2 The Pi symbol, Problem 2.mp4 (226.93 MB)
3 What is a sequence two ways of illustrating sequences.mp4 (24.29 MB)
4 Explicit and recursive ways of defining sequences.mp4 (211.57 MB)
5 Some examples of famous sequences.mp4 (14.86 MB)
6 Recursive to explicit two examples.mp4 (128.44 MB)
7 Arithmetic progressions and arithmetic mean, Problem 3.mp4 (147.16 MB)
8 Geometric progressions and geometric mean, Problem 4.mp4 (180.1 MB)
9 Harmonic progressions and harmonic mean, Problem 5.mp4 (244.87 MB)
1 Bonus Lecture.mp4 (33.6 MB)
1 Plenty of symbols to get acquainted with.mp4 (20.48 MB)
2 Greek letters in mathematics.mp4 (326.82 MB)
3 Latin letters in mathematics.mp4 (225.73 MB)
1 Quite informally about the need for introducing new number types, from N to C.mp4 (353.07 MB)
10 Rational numbers as fractions.mp4 (253.31 MB)
11 Decimal expansion of rational numbers.mp4 (54.76 MB)
12 Finite and periodic decimal expansions.mp4 (131.39 MB)
13 Finite and periodic decimal expansions, Problem 3.mp4 (87.89 MB)
14 Finite and periodic decimal expansions, Problem 4.mp4 (83.02 MB)
15 Finite and periodic decimal expansions, Problem 5.mp4 (195.68 MB)
16 The mysterious irrational numbers.mp4 (223.71 MB)
17 The distributive law, Problem 6.mp4 (159.63 MB)
18 Arithmetic, Problem 7.mp4 (156.38 MB)
19 The distributive law, Problem 8.mp4 (80.17 MB)
2 Natural numbers arithmetic; multiplication has higher precedence than addition.mp4 (229.76 MB)
20 Order of operations (precedence rules), Problem 9.mp4 (341.01 MB)
21 The distributive law and precedence rules don't contradict each other.mp4 (236.19 MB)
22 Arithmetic, Problem 10.mp4 (251.06 MB)
23 Arithmetic, Problem 11.mp4 (189.18 MB)
24 Arithmetic, Problem 12.mp4 (197.31 MB)
25 Future Domain of a function of two variables, Problem 13.mp4 (279.81 MB)
26 Future Values of a function of two variables, Problem 14.mp4 (152.03 MB)
27 Arithmetic, Problem 15.mp4 (410.52 MB)
28 Future the derivative of a polynomial, Problem 16.mp4 (157.13 MB)
3 Commutativity of addition and multiplication.mp4 (66.39 MB)
4 Associativity of addition and multiplication.mp4 (35.55 MB)
5 The distributive law and its consequences.mp4 (204.83 MB)
6 Prime numbers and some divisibility rules.mp4 (29.68 MB)
7 Prime factorization, Problem 1.mp4 (216.44 MB)
8 How to find prime numbers Problem 2.mp4 (239.98 MB)
9 Integer numbers addition, subtraction, and multiplication.mp4 (112.84 MB)
1 Distance is necessary for Calculus.mp4 (34.45 MB)
10 Advanced Unit circles can be strange in Taxi cab metric.mp4 (64.94 MB)
11 Advanced Unit circles can be strange in max metric.mp4 (28.04 MB)
12 Future Why is distance necessary for Calculus.mp4 (54.24 MB)
2 Distance between real numbers; absolute value.mp4 (245.14 MB)
3 Cartesian coordinate system in R2, reflections about axes.mp4 (123.46 MB)
4 Pythagorean Theorem and Euclidean distance between points in the plane.mp4 (201.46 MB)
5 What is triangle inequality and why is it essential for Calculus.mp4 (49 MB)
6 Advanced Distances in metric spaces.mp4 (572.98 MB)
7 Advanced Taxi cab distance Manhattan distance.mp4 (372.42 MB)
8 Advanced Max distance in the plane.mp4 (65.48 MB)
9 Advanced Open ball and deleted (punctured) neighbourhood.mp4 (71.79 MB)
1 Equations unknowns, solutions (roots), solution sets.mp4 (49.65 MB)
10 Linear equations with absolute value, Problem 4.mp4 (73.34 MB)
11 Linear equations with absolute value, Problem 5.mp4 (73.7 MB)
12 Linear equations with absolute value, Problem 6.mp4 (105.94 MB)
13 Future Examples of equations and their solution sets.mp4 (54.33 MB)
14 Equations of straight lines in the plane slope and intercept.mp4 (103.72 MB)
15 Equations of straight lines in the plane, Problem 7.mp4 (240.25 MB)
16 Operations which do not change the solution set of an inequality.mp4 (46.76 MB)
17 Careful with multiplying inequalities by variable expressions.mp4 (39.04 MB)
18 Linear inequalities, Problem 8.mp4 (115.32 MB)
19 How to handle inequalities with absolute value.mp4 (68.47 MB)
2 Inequalities variables, solution sets.mp4 (260.6 MB)
20 Linear inequalities with absolute value, Problem 9.mp4 (221.79 MB)
21 Linear inequalities with absolute value, Problem 10.mp4 (173.76 MB)
22 Linear inequalities with absolute value, Problem 11.mp4 (276.4 MB)
23 Future Equations and inequalities in one variable, in Calculus 1 and 2.mp4 (57.94 MB)
24 Future Equations and inequalities in two variables, in Calculus 3.mp4 (46.72 MB)
25 Advanced A strange circle from Videos 39 and 42, Problem 12.mp4 (74.46 MB)
26 What about systems of linear equations.mp4 (104.45 MB)
3 What does it mean to solve an equation or inequality, to verify a solution.mp4 (190.15 MB)
4 Examples of equations with one unknown and where to find them.mp4 (30.42 MB)
5 Operations which do not change the solution set of an equation.mp4 (138.23 MB)
6 Inconsistent equations and false roots.mp4 (299.47 MB)
7 Linear equations, Problem 1.mp4 (205.52 MB)
8 Linear equations with absolute value, Problem 2.mp4 (557.13 MB)
9 Linear equations with absolute value, Problem 3.mp4 (240.93 MB)
1 Function as a relation between variables independent and dependent.mp4 (81.06 MB)
10 Various ways of describing functions 3 with a table.mp4 (36.65 MB)
11 Various ways of describing functions 4 with a verbal description.mp4 (167.64 MB)
12 Surjections, injections, bijections How to detect injections.mp4 (189.25 MB)
13 Inverse functions.mp4 (218.67 MB)
14 Monotone functions increasing, decreasing, non-decreasing, non-increasing.mp4 (51.4 MB)
15 Bounded functions bounded above and bounded below, maximum, minimum.mp4 (136.26 MB)
16 How to scale, add, subtract, multiply, and divide functions.mp4 (225.08 MB)
17 What is a composition of functions.mp4 (199.46 MB)
18 Future Why is the order of functions in a composition important.mp4 (143.44 MB)
19 Even and odd functions Future integration by inspection.mp4 (66.17 MB)
2 Function as a relation between variables; graph and vertical-line test.mp4 (166.22 MB)
20 Transformations of graphs.mp4 (439.64 MB)
21 Various operations on functions, Problem 1.mp4 (210.09 MB)
22 Inverse function, its domain and range, Problem 2.mp4 (385.83 MB)
23 Two similar functions with different domains, Problem 3.mp4 (149.64 MB)
24 Piecewise functions, Problem 4.mp4 (360.69 MB)
25 Piecewise functions, Problem 5.mp4 (303.45 MB)
26 Piecewise functions, Problem 6.mp4 (130.41 MB)
27 Functions with absolute value, Problem 7.mp4 (433.62 MB)
28 Transformations of graphs, Problem 8.mp4 (80.38 MB)
29 Transformations of graphs, Problem 9.mp4 (23.78 MB)
3 Function as a relation between variables; implicit versus explicit.mp4 (53.05 MB)
30 Heaviside step function, Problem 10.mp4 (42.28 MB)
31 Even and odd functions, Problem 11.mp4 (181.69 MB)
32 Domain and range of a composed function, Problem 12.mp4 (211.05 MB)
33 Advanced Domain and range, Problem 13.mp4 (40.96 MB)
34 Advanced A complicated function, Problem 14.mp4 (216.52 MB)
35 Advanced, Future The derivative of the function from V104, Problem 15.mp4 (152 MB)
36 Even and odd functions, Problem 16.mp4 (392.64 MB)
4 Examples of functions of one variable and where to find them.mp4 (57.96 MB)
5 How to think about sets, their unions, intersections, and differences.mp4 (93 MB)
6 Functions domain, codomain, range.mp4 (30.15 MB)
7 Various ways of describing functions 1 with a formula.mp4 (264.69 MB)
8 Determining the domain three typical issues to remember.mp4 (184.97 MB)
9 Various ways of describing functions 2 with a picture.mp4 (185.2 MB)
1 What is a statement and logical value; open and closed statements.mp4 (82.79 MB)
10 Equivalence versus equality.mp4 (22.49 MB)
11 Tautology as a logical formula.mp4 (113.07 MB)
12 How to verify tautologies.mp4 (122.1 MB)
13 Tautologies, Problem 1.mp4 (220.28 MB)
14 Tautologies, Problem 2.mp4 (171.55 MB)
15 Tautologies, Problem 3.mp4 (182.2 MB)
16 Tautologies, Problem 4.mp4 (102.79 MB)
17 Tautologies, Problem 5.mp4 (165.08 MB)
18 Advanced Tautologies, Problem 6.mp4 (182.85 MB)
19 Existential quantifier THERE EXISTS.mp4 (284.01 MB)
2 To be or not to be in the delta neighbourhood of some point.mp4 (41.02 MB)
20 Universal quantifier FOR ALL; Order matters; Precedence rules.mp4 (323.53 MB)
21 Negations De Morgan's Laws for quantifiers, Problem 7.mp4 (61.98 MB)
22 Logic, Problem 8.mp4 (274.83 MB)
23 Logic, Problem 9.mp4 (346.63 MB)
24 Logic, Problem 10.mp4 (132.49 MB)
25 Future, advanced Sequences, Problem 11.mp4 (279.96 MB)
26 Epsilon-delta, here we come!.mp4 (48.89 MB)
27 Advanced Negation L is not the limit.mp4 (78.21 MB)
3 Unary logical connective Negation NOT.mp4 (89.79 MB)
4 Binary logical connective 1 Conjunction AND.mp4 (221.5 MB)
5 Binary logical connective 2 Disjunction OR.mp4 (158.09 MB)
6 Connectives, Example 5.mp4 (171.44 MB)
7 Binary logical connective 3 Implication IF THEN A necessary condition.mp4 (53.39 MB)
8 Converse, inverse, and contrapositive statements.mp4 (83.85 MB)
9 Binary logical connective 4 Equivalence IFF A necessary and sufficient cond.mp4 (38.02 MB)
1 Primitive notions set, belonging to a set, the empty set.mp4 (66.48 MB)
10 Set difference.mp4 (18.67 MB)
11 Symmetric difference.mp4 (16.76 MB)
12 Complement defined with help of negation.mp4 (363.65 MB)
13 The laws of set theory and the laws of logic.mp4 (58.28 MB)
14 De Morgan's Laws, an illustration and proof.mp4 (193.46 MB)
15 The distributive law, an illustration and proof.mp4 (207.16 MB)
16 Set difference and symmetric difference, Problem 1.mp4 (232.35 MB)
17 Cartesian product of sets.mp4 (51.95 MB)
18 Power set of a given set; an example of Boolean algebra.mp4 (35.69 MB)
19 Cardinality of sets.mp4 (20.92 MB)
2 The universe and its subsets.mp4 (19.29 MB)
20 Cardinality of sets, Problem 2.mp4 (146.39 MB)
21 Optional Equinumerous (equipotent) sets; cardinal numbers.mp4 (34.73 MB)
22 Optional Finite, countable and uncountable sets.mp4 (27.45 MB)
23 Optional Comparing cardinalities of sets, Problem 3.mp4 (512.96 MB)
24 Optional Comparing cardinalities of sets, Problem 4.mp4 (94.14 MB)
25 Inclusion-exclusion principle.mp4 (57.16 MB)
26 Inclusion-exclusion principle, Problem 5.mp4 (207.11 MB)
27 Transposition law and subsets, Problem 6.mp4 (38.34 MB)
3 If you know logic, you know the set theory.mp4 (85.32 MB)
4 Intersection defined with help of conjunction.mp4 (156.44 MB)
5 Union defined with help of disjunction.mp4 (96.73 MB)
6 Equality of sets defined with help of equivalence Axiom of Extensionality.mp4 (29.13 MB)
7 Subset defined with help of implication.mp4 (22.1 MB)
8 The empty set gives a false statement.mp4 (16.56 MB)
9 The universe gives a true statement.mp4 (12.47 MB)
1 Relations in a regular sense.mp4 (44.54 MB)
10 Relation congruence modulo n.mp4 (92.09 MB)
11 Equivalence classes and partitions of a set.mp4 (222.99 MB)
12 More properties of relations irreflexive, antisymmetric, strongly connected.mp4 (205.2 MB)
13 Order relations.mp4 (66.79 MB)
14 Partial orders and Hasse diagrams.mp4 (70.88 MB)
15 Relations, Problem 6.mp4 (373.49 MB)
16 Relations, Problem 7.mp4 (272.04 MB)
17 Relations, Problem 8.mp4 (380.44 MB)
18 Relations, Problem 9.mp4 (147.64 MB)
2 Relations in a mathematical sense.mp4 (46.98 MB)
3 Relation a formal definition and notation.mp4 (52.07 MB)
4 How to plot relations.mp4 (53.21 MB)
5 How to plot relations, Problem 1.mp4 (48.16 MB)
6 Relations on finite sets, and their graphs, Problem 2.mp4 (208.93 MB)
7 RST relations equivalence relations.mp4 (289.43 MB)
8 How to recognize an RST relation from its plot.mp4 (54.7 MB)
9 How to recognize an RST relation on a finite set from the graph.mp4 (245.01 MB)
1 Some early signs.mp4 (45.27 MB)
10 Advanced A theorem about inverse function.mp4 (214.93 MB)
11 Advanced, future A really important theorem about compositions of functions.mp4 (386.5 MB)
2 Each function is a relation, not every relation is a function.mp4 (46.18 MB)
3 Each relation is invertible!.mp4 (65.88 MB)
4 Relations and functions, Problem 1.mp4 (144.71 MB)
5 Relations and functions, Problem 2.mp4 (119.82 MB)
6 Relations and functions, Problem 3.mp4 (268.3 MB)
7 Equality of functions, Problem 4.mp4 (37.67 MB)
8 Surjections and injections, Problem 5.mp4 (537.44 MB)
9 Future Cancellation law for injective functions and why it is important.mp4 (414.62 MB)
1 How we build mathematical theories.mp4 (35.23 MB)
10 Series of equivalences.mp4 (34.16 MB)
11 Proof by contradiction.mp4 (151.37 MB)
12 Existence, uniqueness, counter-examples.mp4 (317.71 MB)
13 Proof of the partition theorem from Video 171.mp4 (496.55 MB)
14 Construction of the natural numbers; Peano and induction.mp4 (425.04 MB)
15 Proof by induction, Problem 1.mp4 (261.78 MB)
16 Proof by induction, Problem 2.mp4 (403.8 MB)
17 Proof by strong induction, Problems 3 and 4.mp4 (634.14 MB)
18 Proof of three statements about natural numbers.mp4 (310 MB)
19 Prove or disprove.mp4 (563.64 MB)
2 Examples of primitive notions and definitions.mp4 (67.63 MB)
20 Define the set of integers using an equivalence relation and the set N.mp4 (264.29 MB)
21 Define the set of rational numbers using an equivalence relation and the set Z.mp4 (310.59 MB)
22 Some algebraic structures and where to find them.mp4 (62.41 MB)
23 Construction of the real numbers.mp4 (416.33 MB)
24 Some examples of proofs directly from the axioms.mp4 (385.72 MB)
25 The glorious and majestic Zero-Product Property.mp4 (166.51 MB)
26 The square root of 2 is irrational.mp4 (164.66 MB)
27 Density of Q and RQ in R.mp4 (121.84 MB)
28 A real number is irrational iff its decimal expansion is infinite aperiodic.mp4 (132.64 MB)
29 Optional Set of real numbers and set of irrational numbers are not countable.mp4 (76.34 MB)
3 Axioms.mp4 (87.7 MB)
30 The last piece of the epsilon-delta definition.mp4 (15.81 MB)
31 Future Proof that the limit of sum is equal to the sum of limits.mp4 (287.29 MB)
4 Theorems, propositions, lemmas, corollaries.mp4 (30.86 MB)
5 Types of proofs.mp4 (70.7 MB)
6 Direct proof (deduction and reduction).mp4 (430.23 MB)
7 Proof by cases.mp4 (215.76 MB)
8 Proof by contrapositive.mp4 (223.32 MB)
9 Proof of the extended version of the Cancellation law from Video 187.mp4 (367.66 MB)
1 The Sigma symbol, Problem 1.mp4 (222.43 MB)
10 Series as sums of the elements in a sequence.mp4 (67.84 MB)
11 Convergent and divergent series.mp4 (22.35 MB)
12 Arithmetic series, Problem 6.mp4 (245.22 MB)
13 Geometric series, Problem 7.mp4 (269.54 MB)
14 Harmonic series, Problem 8.mp4 (78.6 MB)
15 Limit of a sequence; Cauchy sequences.mp4 (100.46 MB)
16 Future Proof that the limit of a sum is equal to the sum of limits.mp4 (162.43 MB)
17 So, what's next.mp4 (55.49 MB)
2 The Pi symbol, Problem 2.mp4 (226.93 MB)
3 What is a sequence two ways of illustrating sequences.mp4 (24.29 MB)
4 Explicit and recursive ways of defining sequences.mp4 (211.57 MB)
5 Some examples of famous sequences.mp4 (14.86 MB)
6 Recursive to explicit two examples.mp4 (128.44 MB)
7 Arithmetic progressions and arithmetic mean, Problem 3.mp4 (147.16 MB)
8 Geometric progressions and geometric mean, Problem 4.mp4 (180.1 MB)
9 Harmonic progressions and harmonic mean, Problem 5.mp4 (244.87 MB)
1 Bonus Lecture.mp4 (33.6 MB)
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