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University of Glasgow Mathematics 2C: Introduction to Real Number Analysis?
Glasgow University was founded in 145 1, proposed by King James II of Scotland and founded by Pope Nicholas V. With a history of nearly 600 years, it is the second oldest public comprehensive university in Scotland (St. Andrews University is the longest in Scotland and was founded in1414).

I believe that students will also be very interested in the courses of this prestigious school. Here, Xiao Si will introduce the course 2C of Glasgow University: Introduction to Real Number Analysis. Interested students don't miss it ~

This course is the first time to introduce real analysis. The main thread running through the whole course is the concept of limit. For sequences and sequences, a precise definition of this concept will be given.

syllabus

Give lectures twice a week. Biweekly course

Examination content

First degree examination (80%) (1 hour 30 points); Course assignments (20%).

Examination time: 65438+February.

Planned goal

Expected learning outcomes of the course.

■ Negative statements involving logical quantifiers; Whether a given conditional statement contains logical quantifiers: determine logically equivalent statements, determine their assumptions and conclusions, and determine their opposites and opposites; Know all kinds of proof methods (for example, direct, opposition, counterexample, contradiction, induction).

■ Prove that the function is bounded or unbounded; It is proved from the first principle that the given number is the limit of the given sequence; Use arithmetic and order attributes to calculate sequence constraints.

■ Given a sequence (including a recursively defined sequence), prove that it is monotonous (or non-monotonous); Using subsequences to establish non-convergence; Determine whether it is convergent or divergent; Determine whether it is absolutely convergent or conditionally convergent.

■ First, determine whether a function is continuous (or discontinuous); Discontinuities are established by using sequential representations; Solving problems by using the theorem of intermediate value and extreme value.

■ State all definitions and results (lemmas, theorems, inferences, propositions) covered in the speech and use them to solve appropriate problems.

■ Prove the results covered in the speech, and apply and modify these proofs in novel situations.