Precalculus 1: Basic notions
A solid preparation for Calculus, with elements of discrete mathematics: logic, sets, functions, relations, and proofs
4.78 (956 reviews)
5 427
students
52 hours
content
May 2025
last update
$84.99
regular price
What you will learn
How to solve problems in chosen Precalculus topics (illustrated with 236 solved problems) and why these methods work.
Repetition of chosen aspects of high school mathematics (basic notions as numbers, functions, sets, equations, and inequalities).
The basic notions will be defined in a more abstract way, and you will get an insight into their place in Calculus and some other branches of university maths.
By the end of this course you will be able to understand all the elements in the epsilon-delta definition of limit, both symbols and the content.
Arithmetic with basic rules (associativity and commutativity of addition and multiplication, distributivity) illustrated for positive integers.
Basic terminology for equations and inequalities, with examples of linear equations and inequalities, with and without absolute value.
Basic concepts related to functions (domain, range, graph, surjection, injection, bijection, inverse, composition) and how to work with them.
Functions: monotone (increasing, decreasing), bounded, even, odd; extremum: maximum, minimum, both local and global.
Geometrical operations on graphs of functions: translations, reflections, shrinking, dilating. Piecewise functions.
Absolute value and its role in computing distances, with geometrical illustrations and functional approach.
Equations of straight lines in the plane: slope and intercept; first glimpse into derivative as the slope of the tangent line, and link to monotonicity.
Introduction to sequences and series; short notation for sum (Sigma) and product (Pi); arithmetic, geometric, and harmonic progressions.
Logic: symbols and rules (tautologies) used for creating mathematical statements, definitions, and proofs.
Set theory: union, intersection, complement, set difference; some important rules and notation.
Relations: RST (equivalence) relations, order relations, functions as relations.
Necessary and sufficient conditions: definition and examples.
Various types of proofs: direct, indirect, by contradiction, induction proof, with some examples.
Building blocks of mathematical theories: axioms, definitions, theorems, propositions, lemmas, corollaries, etc.
Decimal expansion of rational and irrational numbers. Density of Q and R\Q in R.
Cardinality of sets: finite sets, N, Z, Q, R; countable and uncountable sets.
You will also get a solid background for any future studies in Real Analysis and other courses in university mathematics.
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Comidoc Review
Our Verdict
This Precalculus 1: Basic notions course on Udemy offers clear and engaging explanations of a wide range of relevant topics and illustrative problems that help improve mathematical skills. The instructor's commitment to addressing students' questions significantly enhances the value of self-study. However, certain sections, such as examples, basic notions, and historical context could benefit from improved organization or expanded content for enhanced clarity and engagement. Overall, this course provides solid foundational knowledge—though it may be helpful to integrate additional resources to connect abstract concepts with real-world applications.
What We Liked
- Covers a wide range of relevant Precalculus topics with 236 illustrative problems
- Clear and engaging explanations of mathematical operations that help improve skills
- Well-organized course structure, starting from basics to advanced concepts
- Instructor provides in-depth answers to questions, alleviating disadvantages of self-study
Potential Drawbacks
- Some examples could use more detailed explanations for clarity and understanding
- Basic notions section could benefit from expanded content or integration within sections
- Course introduction and historical context of symbols sections can feel too brief or detached
- Lack of practical, real-world applications or fun facts to connect abstract topics with daily life
Related Topics
4380230
udemy ID
03/11/2021
course created date
04/02/2022
course indexed date
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