Mathematics BSc
Course description
2013. Analysis 1
Hours
lect+pc
Credits
lect+pc
Assessment Specialization Course code
lect/pc
Semester Status
3 + 4 3 + 5 exam +
all mm1c1an1
mm1c2an1
1 alternative
Strong Weak Prerequisites
Lecture
Weak:
practice class
Remarks
• You have to take exactly one of the following two equivalent sets of courses: {Analysis 1, Analysis 2} or {Calculus 1, Calculus 2, Foundations of analysis}.
Syllabus designed by:
Prerequisites
A thorough understanding of High school mathematics.
Syllabus
• Basic concepts of mathematical logic. Some basic tools for proving theorems. Classical inequalities. Sets, functions sequences.
• Axioms of the real numbers. Models of real numbers. Least upper bound and greatest lower bound. Powers.
• Convergence of sequences. Sequences tending to infinity. Basic properties of convergent sequences. Monotone sequences. The limit superior and limit inferior. The Bolzano-Weierstrass theorem. Cauchy sequences.
• Countable and uncountable sets.
• Convexity and monotonicity of real functions. Limits of functions. Continuous functions. Interior points, cluster points and isolated points.
• Global properties of continuous functions on closed intervals. Monotonic functions and continuous functions. Convex functions and continuous functions.
• Some elementary functions (polynomials, rational functions, trigonometric functions, hyperbolic functions).