I. Background Information II. Pre-reading Activities III. Text Analysis– Structure IV. Intensive Reading V. Writing Skill VI. Exercises

I. Reading skill II. Fast reading. III. Structure of the text. IV. Important Words V. Detailed study of Text VI. Exercises

1 The How, When, and Why of Mathematics Spotlight: George Polya Tips on Doing Homework 2 Logically Speaking 3 Introducing the Contrapositive and Converse 4 Set Notation and Quantifiers Tips on Quantification 5 Proof Techniques Tips on Definitions …… 10 Relations Tips on Reading Mathematics 11 Partitions Tips on Putting It All Together 12 Order in the Reals 13 Consequences of the Completeness of R Tips: You Solved ItNow What? 14 Functions, Domain, and Range Spotlight: The Definition of Function 15 Functions, One-to-One, and Onto 16 Inverses 17 Images and Inverse Images Spotlight: Minimum or Infimum? 18 Mathematical Induction 19 Sequences 20 Convergence of Sequences of Real Numbers 21 Equivalent Sets 22 Finite Sets and an Infinite Set 23 Countable and Uncountable Sets 24 The Cantor–Schroder–Bernstein Theorem Spotlight: The Continuum Hypothesis ……

Warm Up Global Reading Detailed Reading Consolidation Activities Text Appreciation Further Enhancement

1 Warming-up 2 Reading A 3 Reading B 4 Listening & Speaking 5 Writing 6 Mini-project 7 Language Lab

Text A Reading Comprehension Vocabulary Summary Structure Translation Grammar Focus Speech New Words and Expressions Text B Vocabulary New Words and Expressions Comprehension Reading

1 Warming-up 2 Reading A 3 Reading B 7 Language Lab 4 Listening & Speaking 5 Writing

Part I Lead-in Part II In-Class Reading Part III After-Class Reading

Part I Lead-in (Task 1-5) Part II In-Class Reading (Text Structure; Word Study; Sentence Study) Part III After-Class Reading (Passage One; Passage Two)

1. Warm-up Questions 2. Background Knowledge 3. Text Analysis 4. Exercises 5. Questions For Discussion