Precalculus 1: Basic notions

🌟 Precalculus 1: Basic Notions 🎓

Course Overview:

Embark on a journey through the fundamental concepts of Precalculus, which will lay the groundwork for your future studies in Calculus. This course intertwines key elements of discrete mathematics, including logic, sets, functions, relations, and proofs. Precalculus 1 is designed to enhance your understanding and proficiency in mathematical concepts essential for university-level mathematics.

What You'll Learn:

S1. Introduction to the Course 📘

• An overview of the course content and strategies for effective studying.

S2. Magical Letters and Symbols ✨

• Understand Greek and Latin letters and their significance in mathematics.
• Familiarize yourself with essential mathematical symbols that will be used throughout this course.

S3. Numbers and Arithmetic 🧮

• Explore the different kinds of numbers and their arithmetic, including natural, integer, rational, irrational, real numbers, and more.

S4. Absolute Value and Distances 🌍

• Master the Cartesian coordinate system and learn how to calculate distances using absolute values in various metric spaces.

S5. Equations and Inequalities 📈

• Dive into solving linear equations, including those with absolute values, and understand the concept of solution sets.

S6. Functions 📈

• Delve into the world of functions, covering domain, range, graph interpretation, function types, and transformations.

S7. Logic 🧠

• Gain a solid understanding of logical symbols, rules, quantifiers, and proof techniques that are fundamental to mathematical reasoning.

S8. Sets 🔄

• Learn about set theory, operations like union, intersection, and the importance of cardinality and inclusion-exclusion principles.

S9. Relations 🌀

• Explore different types of relations, including RST properties and the concept of equivalence classes and order relations.

S10. Functions as Relations ↔️

• Understand how functions can be viewed as special kinds of relations between sets, exploring injections, surjections, and bijections.

S11. Axioms, Definitions, Theorems, and Proofs 📚

• Decipher the differences between axioms, definitions, theorems, and more, and learn various types of proofs to apply in your problem-solving.

S12. Sequences and Series; AP, GP, HP 📉

• Discover how to work with sequences and series, including arithmetic, geometric, and harmonic progressions.

S13. Extras 🎉

• Get a preview of the additional resources we offer and a glimpse into future course plans.

Additional Resources:

• Detailed Course Content: A comprehensive list of all videos and problems, including titles and texts for each problem, is provided in the resource file "001 List_of_all_Videos_and_Problems_Precalculus_1.pdf". This content is fully explained in the first video, "Introduction to the Course."

Important Notes:

• Exam Preparation: Ensure you align with your professor on the specific parts of the course that will be relevant for your final exam, as requirements can vary greatly.

• Course Content Updates: Keep an eye out for updates and future courses, which we plan to release (with a disclaimer that these are hypothetical and subject to change).

Join us on this mathematical adventure where you'll gain the skills necessary to excel in Precalculus and beyond. With expertly crafted lessons and a wealth of resources at your fingertips, you're set for success! 🌟