This audio focuses on the concept of similar triangles. It begins by outlining fundamental definitions and theorems related to triangle congruence, such as SSS, SAS, ASA, and AAS. The podcast then transitions to exploring properties of similar triangles, including angle and side ratios. Several worked-out problems illustrate how to apply these conc…

This audio introduces fundamental concepts related to angles, starting with definitions of straight and right angles. It then covers complementary and supplementary angles and explores properties of interior and exterior angles in polygons. The audio further explains relationships between angles formed by transversals intersecting parallel lines an…

The audio focuses on fundamental concepts within probability. It introduces the definition of conditional probability and Bayes' Theorem, illustrating their application through worked examples involving dice rolls and event dependencies. The audio then explores expected value, linearity of expectation, and problems requiring the calculation of expe…

This audio source focuses on binomials and recursion, two fundamental concepts in mathematics often encountered in these competitions. The audio introduces the binomial theorem and related identities, such as Pascal's Identity and the Hockey Stick Identity, providing formulas and examples. It then transitions to recursion, defining it and illustrat…

This audio explores methods for counting and arranging items under various constraints. It introduces fundamental combinatorial concepts such as calculating the number of paths on a grid and determining the arrangements of letters or objects. Several example problems illustrate these principles, including distributing candies, arranging dice rolls,…

This podcast on combinatorics introduces fundamental principles for counting, such as casework and complementary counting. It provides formulas and theorems for permutations with repeated elements and combinations. Several examples and problems illustrate how to calculate the number of ways to arrange letters in words, form license plates, select i…

Welcome to Episode 12 of Season 1: Unlocking Number Theory! This video contains mathematical problems and solutions. The problems cover a range of topics including logarithms, floor functions, and recursive sequences. Each problem is sourced, indicating where it originated. Detailed solutions are provided, often utilizing algebraic manipulation and…

Welcome to Episode 11 of Season 1: Unlocking Number Theory! This video covers inequalities and functional equations, along with telescoping series, for math competition preparation. It introduces key theorems like the AM-GM and Cauchy-Schwarz inequalities and demonstrates their use in problem-solving. The text also explores various functional equat…

Welcome to Episode 10 of Season 1: Unlocking Number Theory! This episode contains mathematical problems and solutions aimed at students preparing for the AMC 10 and AMC 12 competitions. It focuses on various problem-solving techniques, including factoring, manipulating equations, and utilizing substitutions. Specific examples cover topics like diff…

Welcome to Episode 9 of Season 1: Unlocking Number Theory! This episode presents a series of logarithm problems and their solutions, demonstrating various techniques for solving logarithmic equations. Key rules and formulas are introduced, including the change of base formula. The problems cover a range of complexity, from basic logarithmic identit…

Welcome to Episode 8 of Season 1: Unlocking Number Theory! This video presents solutions to various math problems, primarily focusing on polynomial equations. Vieta's Theorem is frequently applied to find relationships between polynomial coefficients and their roots. The problems explore concepts such as finding the sum of roots, determining the sm…

Welcome to Episode 7 of Season 1: Unlocking Number Theory! This episode presents mathematical problems and solutions focusing on arithmetic, geometric, and arithmetic-geometric sequences. Key concepts covered include relevant formulas, such as the sum of arithmetic and geometric series. Examples illustrate problem-solving techniques using these for…

Welcome to Episode 6 of Season 1: Unlocking Number Theory! This episode dives into various number theory problems, primarily focusing on the application of modular arithmetic and the Chinese Remainder Theorem. Many problems involve finding remainders, solving congruences, or determining properties of integers. The solutions demonstrate techniques f…

Welcome to Episode 5 of Season 1: Unlocking Number Theory! This episode focuses on Euler's totient function and Fermat's Little Theorem, illustrating their applications through examples and problem-solving. The author employs modular arithmetic and prime factorization to solve a problem involving finding the largest integer with specific properties…

Welcome to Episode 4 of Season 1: Unlocking Number Theory! This episode focuses on unit digits in number theory problems. Specific examples illustrate how to find patterns in unit digits of powers and sums, using techniques like modular arithmetic. The text introduces modular arithmetic as a tool for solving these problems, showing how to find rema…

Welcome to Episode 3 of Season 1: Unlocking Number Theory! This episode presents solutions to several math problems involving number bases and other mathematical concepts. Specific problems include finding remainders after division, converting between different number bases (such as base 10, base 8, and base 11), and identifying palindromic numbers…

Welcome to Episode 2 of Season 1: Unlocking Number Theory! In this episode, we delve into the fascinating world of palindromes—numbers that read the same forwards and backwards. We'll start by defining palindromes and sharing illustrative examples before diving into problem-solving techniques that involve these unique numbers. Our discussion includ…

Welcome to Season 1: Unlocking Number Theory! In Episode 1 of this season, join us as we dive into the fascinating world of number theory! In this episode, we explore essential concepts like prime and composite numbers, divisibility rules, and methods for finding least common multiples (LCMs) and greatest common divisors (GCDs). Through clear expla…