PhD student in Maths & Quantum Computing | Expert in SAT, ACT, Calculus (all levels), Algebra, Geometry & Trig, Probability, and many others.

The student and tutor worked through several challenging math problems, including geometry with coordinate points and a complex word problem involving meeting durations and breaks. The session focused on algebraic equation setup, solving, and applying logical deductions to find integer solutions. The tutor assigned a similar problem for the student to practice.

The Student and Tutor reviewed mathematical concepts, starting with a discussion on the definition of infinity and its paradoxes. They worked through a logarithm series problem, attempting both a proof-based derivation and a more direct calculation. The session also included a rapid-fire practice of various applied math problems and culminated in deriving the general formula for a quadratic sequence and setting up equations to solve for its constants, which was assigned as homework.

Student and Tutor reviewed a homework problem focused on calculating the sum of floor functions of base-2 logarithms. They discussed the properties of floor and ceiling functions, and explored methods for formulating the sum algebraically. The session also included an extensive theoretical discussion on the nature of infinity and divergent series, with the Tutor planning to send a solution for the logarithm problem and additional proofs regarding infinite series.

Student and Tutor engaged in a comprehensive mathematics problem-solving session. They practiced a variety of topics including probability, algebraic equations, geometry, averages, combinatorics, and speed-distance-time calculations. The session concluded with an introduction to the Euclidean algorithm for finding the HCF, which was assigned as follow-up work.

The Student and Tutor worked on two complex coordinate geometry problems from a textbook, focusing on circular equations and optimization. They first calculated the shortest path between two points that touches a circle, then found the maximum value of a linear expression constrained by a circular equation. The session concluded with an introduction to vectors to provide foundational knowledge for related formulas, and the Student was assigned to explore vectors further and attempt a probability question for homework.

The session started with introductions and a discussion of the Student's goals to apply mathematics, specifically probability, to real-world scenarios. The Tutor assessed the Student's understanding of probability through a series of problems involving dice, cards, and knockout tournaments, and introduced relevant mathematical resources. They also discussed future session frequency, aiming for weekly classes to maintain skill sharpness.