Precalculus Mate 3018 (or its two semester variant 3171+3172) is a “pre-mathematics” course reviewing topics which should have been —but which frequently are not— covered in the high school. Warning: The one semester variant. Math 3018, is intended for students whose college board score in mathematics is greater than 720. A grade of **A** in the remedial course Math 3001 is **NOT** , on its own, sufficient preparation for Math 3018. Indeed, the two semester sequence Math 3171-72 is more suitable for most students.

- Course Philosophy
- Generic Course Objectives
- Classroom Behaviour
- On the use of electronic aparati
- Recomendaciones para Estudiantes Nuevos
- In Praise of Lectures

## 2020-2021– Semester II

### Detailed Syllabi with Formulae

### Old Exams

- Math 3171 – Exam I | Math 3171 – Exam II |Math 3171 – Exam III | Math 3171 – Exam IV
- Math 3018 – Exam I | Math 3018 – Exam II |Math 3018 – Exam III | Math 3018 – Exam IV

### Textbooks

- (Free) Precalculus Book by David Santos
- (Free) Ossifrage-And-Algebra-2007 by David Santos
- (Free) Pre-y Cálculo Criollos (Spanish Version) by David Santos
- (Free) Andragogic Propaedeutic Mathematics by David Santos
- (Free) Differential Calculus by David Santos

### Weekly Readings and Exercises

- On Definition (Definition according to Aristotle)
- On Truth
- On implication
- Review of Elementary Set Theory and Logic
- Binary Relations and Functions
- Fractions
- Mathematical Induction
- Properties of the real numbers
- Order and Inequalities
- Straight Lines
- The Plane
- Some Standard Forms of the Straight Line
- Graphing examples
- Image of a function
- Composition of Functions
- The Circle
- The Parabola
- Exponential functions–review
- Sequences
- Limits of sequences
- The Complex Numbers
- The Synthetic Division Algorithm
- Notes on Trigonometry

### Additional Reading and Exercises

- Truth tables
- On validity
- A list of tautologies
- Greek Alphabet
- LateX Examples-pdf
- Download LaTex Source Code
- Unix File Permissions
- Logic Set Correspondence
- Venn Diagrams
- Teorema Binomial
- Real Valued Functions
- Funciónes Inversas
- Polinomios
- Trigonometría I
- Trigonometría II
- Triángulos

### Notes on the Bibliography

A Bibliography is included in the course syllabus above. Please read the following remarks before deciding on which books to purchase.

The great price (and weight) of precalculus textbooks bears no relation to their academic quality. The very excellent *Elementary Algebra* and *Precalculus* texts by David Santos can be legally downloaded (See syllabus for a link). For math majors and students aiming to achieve a good scientific level, these are preferable to the current official text.

The following books contain material relevant to the course. The translation of *Mathematics, Japanese grade 9 * by Kunihiko Kodaira is an excellent review of material from high school algebra and geometry. It also includes a section on probability and statistics. *Mathematics, Japanese grade 10* contains most, though not all, of the material in MATH 3171 as well as some trigonometry from Math 3172. It manages to achieve in 200 pages what the recommended text struggles to do in 1000. The text *Algebra and Geometry, Japanese Grade 11* covers plane and solid geometry, vectors and matrices.

The text *Introductory Analysis* by Dolciani et al. has been used by the Department in previous years so it can be obtained at a modest price in the street or from Amazon (for less than $10 used). It is more carefully written than the official text and at a higher mathematical level.

As its title suggests, the book *Foundations of Mathematics* by Stewart and Tall gives a more profound view of the foundations of Mathematics and the construction of the numbers than the other texts. Any student who is serious about achieving a good level in Mathematics should know the material in this book. If you are a math major and cannot manage the material in this book you should probably change major. Conversely, if you are not a math major and you like the material in this book you should consider switching to math.