Welcome to the captivating journey of "Foundations of Mathematical Thinking." This course invites you to delve into the profound world of mathematical concepts and logical reasoning, setting the stage for a transformative intellectual adventure. Picture yourself stepping into a realm where sets, logic, linear algebra, calculus, and statistics converge to equip you with a robust foundation in mathematical thinking.

As you begin this course, you'll first explore the elegant realm of set theory, where you'll grapple with the fundamental definitions of sets, decipher set notation, and engage in set operations such as union, intersection, and complement. Moving to propositional logic, you'll unravel the intricacies of logical propositions, truth tables, and the nuances of logical implication and equivalence. Predicate logic will introduce you to the power of quantifiers and predicate notation, enabling you to translate complex English statements into precise logical expressions.

In the second part, you'll journey into the heart of linear algebra for machine learning, a field essential in modern data analysis. You'll master vector and matrix operations, delve into the properties of eigenvalues and eigenvectors, and understand the magic of diagonalization. Linear transformations will become second nature as you explore their properties, matrix representations, and the flexibility of changing bases.

The third part of the course will introduce you to the calculus and optimization, where you'll delve into limits, continuity, and the fascinating Intermediate Value Theorem. Derivatives will be your tool for analyzing the behavior of functions, and you'll learn the rules of differentiation and their applications, including finding maxima and minima. Integral calculus will enable you to calculate areas, solve optimization problems, and understand the fundamental theorem of calculus.

Finally, the course will immerse you in the realm of probability and statistics, essential in making data-driven decisions. You'll explore probability basics, understand different probability distributions, including the ubiquitous normal distribution, and delve into statistical inference, where you'll learn hypothesis testing, confidence intervals, and maximum likelihood estimation.

Whether you're an aspiring mathematician, a data scientist, an engineer, or simply someone captivated by the beauty of mathematical thinking, this course is your gateway to unlocking the language of the universe.