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This course presents a general view of a number of mathematical topics to a non-technical audience, often relating the mathematical topics to a historical context, and providing students with an opportunity to engage with the mathematics at an introductory level. Although some variation in topics covered may take place among different instructors at different campuses, an example of such a course focuses on a number theory theme throughout the course, beginning with the Greeks' view of integers, the concept of divisors, the calculation of greatest common divisors (which originates with Euclid), the significance of the prime numbers, the infinitude of the set of prime numbers (also known to the ancient Greeks), work on perfect numbers (which continues to be a topic of research today), and the work of Pythagoras and his famous Theorem. The course then transitions to the work of European mathematicians such as Euler and Gauss, including work on sums of two squares (which generalizes the Pythagorean Theorem), and then considering Euler's phi function, congruences, and applications to cryptography.
Development of a thorough understanding and technical mastery of foundations of classical analysis in the framework of metric spaces. MATH 403H Honors Classical Analysis I (3)The central aim of this course is to develop thorough understanding and technical mastery of foundations of classical analysis in the framework of metric spaces rather than multidimensional Euclidean spaces. This level of abstraction is essential since it is in the background of functional analysis, a fundamental tool for modern mathematics and physics. Another motivation for studying analysis in this wider context is that many general results about functions of one or several real variables are more easily grasped at this more abstract level, and, besides, the same methods and techniques are applicable to a wider class of problems, e.g. to the study of function spaces. This approach also brings to high relief some of the fundamental connections between analysis on one hand and (higher) algebra and geometry on the other. This course is a sequel to Math 312H; it is highly recommended to all mathematics, physics and natural sciences majors who are graduate school bound, and is a great opportunity for all Schreyer Scholars. The following topics will be covered: Metric spaces (topology, convergence, Cauchy sequences and completeness); Maps between metric spaces (continuous maps and homeomorphisms, stronger continuity properties:uniform continuity, Hoelder and Lipschitz continuity, contraction mapping principle, points of discontinuity and the Baire Category Theorem); Compact metric spaces (continuity and compactness, connectedness, total boundedness, coverings and Lebesgue number, perfect metric spaces, characterization of Cantor sets, fractals); Function spaces (spaces of continuous maps, uniform continuity and equicontinuity,Arzela-Ascoli Theorem, uniform approximation by polynomials. Stone-Weierstrass Theorem).
I never watch the Japanese one, some of the viewer who watch the Japanese one will think something else after watch this. Just like when you watch fincher's dragon tattoo after the Swedish one, which one is better So, I'm hardly rate ten star because no such perfect movie in this world, this movie either. But, something all moviegoers need is the movie that have some kind of spirit, which it can hold you to stay on your seat till the end of credit. Make your mind think like this is not right What's going on What will happen next Should sequeling this! A love movie that doesn't need ''I love you'' quote.What I don't like about this movie is,they should make it more longer,because we love to see what will happen to the character's life. I'm so sad, a good romance-detective-mystery movie. Highly recommended!! 153554b96e
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