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Precalculus 1: Basic notions

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$9.99 Coupon code for Precalculus 1: Basic notions Udemy Course. This is an exclusive discount coupon from the course instructor, it will be active for few days. Check ENROLL NOW button to get a maximum discount. We manually verified coupon code on July 3rd, 2024 .

Mathematics from high school to university
Instructed by Hania Uscka-Wehlou 52 hours on-demand video & 380 downloadable resources

What you’ll 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.

Who this course is for:

  • Students who plan to study Calculus, Real Analysis, Discrete Mathematics or Abstract Algebra
  • High school students curious about university mathematics; the course is intended for purchase by adults for these students
  • Everybody who wants to brush up their high school maths and gain a deeper understanding of the subject
  • College and university students studying advanced courses, who want to understand all the details they might have missed in their earlier education

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