This course begins with an in-depth study of the fundamental concepts of calculus and linear algebra, with special emphasis on the fundamentals of mathematics. The use and understanding of proof and abstract concepts will allow students to develop analytical skills which will provide a basis for further study in fundamental mathematics and for a wide range of quantitative fields such as actuarial studies, computer science, economics, engineering, physics and statistics Base.

Two topics covered

Calculus/Analysis – supremum and lower bounds on the set of real numbers, completeness, Riemann-Darbe definition of integrals, introductory formal logic, real number axioms, sequences, convergence, limits, continuity, related real number analysis theorems, Including the monotone convergence theorem and the Bolzano-Weilstrass theorem for sequences of real numbers, the existence of extreme values, differentiation, applications of derivatives, proofs of the Fundamental Theorem of Calculus, Taylor polynomials, l’Hospital rule, inverse functions;

Linear Algebra – Solve linear equations, matrix equations, linear independence, matrix transformations, matrix operations, matrix inverses, abstract vector spaces, subspaces, dimension and rank, determinants, Kramer’s rule, complex numbers.

Three Learning Outcomes

Upon successful completion, students will have the knowledge and skills to:

1. Explain the fundamental concepts of calculus and linear algebra and their role in modern mathematical and applied contexts.
2. Demonstrate accurate and efficient use of calculus and linear algebra techniques.
3. Demonstrate the ability to reason mathematically by analyzing, proving and explaining concepts and theorems of calculus and linear algebra.
4. Solve problems using techniques of calculus and linear algebra applied to a variety of situations in physics, engineering, and other mathematical settings.

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