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所在平台: Udemy |
课程主页: https://www.udemy.com/course/precalculus-1/
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课程名称：前置数学 1：基本概念 课程概述：前置数学 1：基本概念旨在帮助学习者从高中数学过渡到大学级别的数学学习。该课程分为多个模块，包括课程介绍、数学符号及其使用、各种数的运算、绝对值与距离、方程与不等式、函数、逻辑、集合、关系、函数作为关系、公理与定理、以及数列与级数等内容。 主要学习内容： 1. **课程介绍**：了解课程内容及最佳学习方法。 2. **神奇的字母与符号**：学习希腊字母和拉丁字母在数学中的用法，掌握课程中常用的数学符号。 3. **数字与算术**：认识自然数、整数、有理数、无理数、实数等不同类型的数字及其运算。 4. **绝对值与距离**：学习笛卡尔坐标系及绝对值的概念，理解点的坐标和距离的测量。 5. **方程与不等式**：解析方程与不等式（重点是线性方程及其绝对值形式），及其解集的表示。 6. **函数**：探讨函数的定义、图形、单调性及其运算与变换。 7. **逻辑**：了解逻辑符号及其含义，学习基本的逻辑规则和证明方法。 8. **集合**：掌握集合论的基本术语，包括并集、交集、子集等。 9. **关系**：研究二元关系及其分类，如自反-对称-传递关系。 10. **函数作为关系**：理解函数的定义，以及其在集合之间的映射。 11. **公理、定义、定理和证明**：了解这些术语的含义，学习多种类型的证明方法。 12. **数列与级数；等差、等比及调和数列**：学习数列和级数的基本概念及其表示。 请务必与您的教授确认您在期末考试中需要的课程内容，这可能因国家、大学及年份而异。课程包含237个视频和236个问题的详细描述，资源文件《001 List_of_all_Videos_and_Problems_Precalculus_1.pdf》中有更详细的信息。
Precalculus 1: Basic notionsMathematics from high school to universityS1. Introduction to the courseYou will learn: about this course: its content and the optimal way of studying.S2. Magical letters and symbolsYou will learn: Greek and Latin letters and their usage in mathematics; mathematical symbols you will learn during this course.S3. Numbers and arithmeticYou will learn: about different kinds of numbers (natural numbers, integers, rational numbers, irrational numbers, real numbers) and their arithmetic.S4. Absolute value and distancesYou will learn: Cartesian coordinate system: the axes, the unit, the origin, the coordinates of points, coordinates after reflections about the axes and the origin; absolute value as the distance from a real number to zero; absolute value for measuring distances; distances in abstract metric spaces.S5. Equations and inequalitiesYou will learn: different ways of looking at equations and inequalities (as something to be solved, or as something what describes certain sets), with focus on linear equations and inequalities containing absolute value. Solution sets as subsets of R or R^2.S6. FunctionsYou will learn: about functions: various ways of defining functions; domain, range, graph; x- and y-intercepts; surjections, injections, bijections, inverse functions; increasing and decreasing (monotone) functions; bounded functions; arithmetic operations on functions; compositions of functions; odd and even functions; transformations of graphs.S7. LogicYou will learn: the meaning of the symbols used in logic; conjunction, disjunction, implication, equivalence, negation; basic rules of logic (tautologies) and how to prove them; two kinds of quantifiers: existential and universal; necessary and sufficient conditions.S8. SetsYou will learn: the basic terms and formulas from the Set Theory and the link to Logic; union, intersection, set difference, subset, complement; cardinality of a set; Inclusion-exclusion principle.S9. RelationsYou will learn: about binary relations generally, and specifically about RST (Reflexive-Symmetric-Transitive) relations, equivalence classes, and about order (partial order) relations.S10. Functions as relationsYou will learn: definition of a function as relation between sets: domain and co-domain; injections, surjections, bijections, inverse functions.S11. Axioms, definitions, theorems, and proofsYou will learn: the meaning of words axiom, definition, theorem, lemma, proposition, corollary, proof; Various types of proofs with some examples: direct proof, proof by induction, indirect proof, proof by contradiction.S12. Sequences and series; AP, GP, HPYou will learn: how to use the symbols Sigma and Pi; you will also get an introduction to sequences and series, with some examples; arithmetic, geometric, and harmonic progressions.Make sure that you check with your professor what parts of the course you will need for your final exam. Such things vary from country to country, from university to university, and they can even vary from year to year at the same university.A detailed description of the content of the course, with all the 237 videos and their titles, and with the texts of all the 236 problems solved during this course, is presented in the resource file "001 List_of_all_Videos_and_Problems_Precalculus_1.pdf" under video 1 ("Introduction to the course"). This content is also presented in video 1.
