Generating Functions: Advanced Counting

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Fibonacci numbers and the golden ratio

Explores the Fibonacci sequence, identities, golden ratio, and explicit formulas.

Functions of Several Real Variables

Explores real functions of several real variables, limits, and algebraic operations.

Sobolev Spaces in Higher Dimensions

Explores Sobolev spaces in higher dimensions, discussing derivatives, properties, and challenges with continuity.

Limits of Functions in Several Variables

Explores limits of functions in several real variables, including the two gendarmes theorem and the minimum and maximum theorem on compact sets.

Frobenius Method: Illustration around an Ordinary Point

Covers the Frobenius method for solving ODEs around an ordinary point.

Limit of Functions: Convergence and Boundedness

Explores limits, convergence, and boundedness of functions and sequences.

Ramanujan Graphs: Generating Functions and Expander Graphs

Explores Ramanujan graphs, generating functions, non-backtracking walks, and expander graphs in relation to NP-hard problems.

Fundamental Limits of Gradient-Based Learning

Delves into the fundamental limits of gradient-based learning on neural networks, covering topics such as binomial theorem, exponential series, and moment-generating functions.

Partial Derivatives and Functions

Covers partial derivatives for functions of one and two variables, emphasizing their importance and calculation.

Taylor Series: Convergence and Applications

Explores Taylor series convergence and applications in approximating functions and solving mathematical problems.