In our introductory lecture, Dr. Snellman highlights the practical value of applied mathematics, showing how understanding the principles behind algorithms and optimization can provide a competitive edge. We explore real-world applications such as business optimization, medical imaging, drug discovery, and autonomous vehicles, illustrating how applied mathematics is transforming these fields. The lecture concludes with inspiring examples of students who used their mathematical knowledge to launch exceptional careers, reinforcing that anyone can master these concepts to build impactful, marketable skills.

In lecture two, Dr. Snellman introduces the concept of derivatives, their computation rules, and their significance in modern mathematics and data science. The lecture covers various derivative rules including the power rule, chain rule, product rule, and quotient rule, while emphasizing their applications in optimization problems and machine learning. The discussion concludes with an explanation of Euler's number (e) and its unique property in exponential functions, demonstrating how mathematical concepts interconnect to solve complex problems.

In lecture three, we explore the importance of derivatives in optimization problems, demonstrating how nearly everything in life can be viewed through the lens of optimization—from choosing lunch locations to taking exams. We learn that finding where derivatives equal zero helps identify peaks and valleys in functions, which correspond to maximum and minimum values crucial for real-world applications like minimizing error in machine learning models. Dr. Snellman introduces Newton's method, one of the most important algorithms in mathematics, and highlights cases where we must be careful using it.