羞辱
发表于 2025-3-23 11:25:48
Textbook 20161st editiontem. The entire text (omitting some less central topics) can be taught in two quarters of 25–30 lectures each. The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory..
细胞
发表于 2025-3-23 14:06:26
http://reply.papertrans.cn/16/1562/156113/156113_12.png
exophthalmos
发表于 2025-3-23 20:48:34
Starting at the beginning: The natural numbers,e will have to begin at the very basics - indeed, we will go back to the concept of . and what their properties are. Of course, you have dealt with numbers for over ten years and you know how to manipulate the rules of algebra to simplify any expression involving numbers, but we will now turn to a m
高尔夫
发表于 2025-3-23 22:20:24
http://reply.papertrans.cn/16/1562/156113/156113_14.png
省略
发表于 2025-3-24 05:40:44
The real numbers,rationals ... We defined the natural numbers using the five Peano axioms, and postulated that such a number system existed; this is plausible, since the natural numbers correspond to the very intuitive and fundamental notion of .. Using that number system one could then recursively define addition a
使迷醉
发表于 2025-3-24 08:01:03
http://reply.papertrans.cn/16/1562/156113/156113_16.png
Spinal-Fusion
发表于 2025-3-24 14:03:32
Continuous functions on R,number .. to each natural number .. We then did various things with these functions from . to ., such as take their limit at infinity (if the function was convergent), or form suprema, infima, etc., or computed the sum of all the elements in the sequence (again, assuming the series was convergent).
fulcrum
发表于 2025-3-24 16:33:24
Differentiation of functions,using limits, in contrast to the geometric definition of derivatives, which uses tangents. The advantage of working analytically is that (a) we do not need to know the axioms of geometry, and (b) these definitions can be modified to handle functions of several variables, or functions whose values ar
Axillary
发表于 2025-3-24 22:02:24
http://reply.papertrans.cn/16/1562/156113/156113_19.png
–LOUS
发表于 2025-3-25 00:30:32
http://reply.papertrans.cn/16/1562/156113/156113_20.png