Algebra 101: Beginner to Intermediate Level

Unlock the Power of Algebra: From Basics to Brilliance

Algebra 101: Beginner to Intermediate Level

Unlock the Power of Algebra: From Basics to Brilliance

Unleash your mathematical potential with Algebra 101, where learning transcends traditional boundaries and transforms into a journey of discovery. Designed for both budding students and lifelong learners, this course is your gateway to unraveling the complexities of everyday problem-solving through the power of algebra. Experience a paradigm shift in how you perceive numbers and their relationships. Through intuitive insights and expert guidance, master the art of logical reasoning and abstract thinking, laying the groundwork for future success in any field. This isn't just another online class; it's an immersive experience that builds confidence and competence. Embrace this opportunity to elevate your analytical skills and redefine your future with unparalleled mastery. Your algebraic adventure awaits--enroll now and start your transformation.

Self Paced • Online Class • 25 Hours

$120

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OVERVIEW

CURRICULUM

Algebra 101: Beginner to Intermediate Level

Name: Algebra 101: Beginner to Intermediate Level
Price: 95.00 USD

CRN: 9770451

Lesson 1. Understanding the Language and Significance of Algebra

Algebra serves as a systematic study of numbers and their abstractions, providing foundational knowledge essential for understanding trigonometry and calculus. By mastering algebraic terminology and operations like variables and functions, students build a framework for tackling mathematical structures.

Lesson 2. An Introduction to the Set of Real Numbers

The extensive set of real numbers includes all possible point placements on an infinite number line, comprising subsets such as natural, whole, and rational numbers, while also excluding infinities and imaginary quantities. These real numbers endow mathematical operations with specific properties like associativity and inverse, crucial for equation manipulation.

Lesson 3. Foundations of Algebra: Mastering Basic Operations

The essence of algebra lies in its ability to transform expressions while conserving their equality, necessitating a grasp of operations involving variables. This lesson guides students through orderly operations, equality maintenance, and strategic substitution for simplifying complex expressions.

Lesson 4. Functions: The Building Blocks of Algebra

This lesson introduces functions as a relation between sets of numbers, highlighting key concepts such as domains and ranges, and explores the properties of functions, including one-to-one functions and the vertical and horizontal line tests. By mastering these core ideas, students progress towards understanding and manipulating functions, allowing for more advanced algebraic applications.

Lesson 5. Linear Equations Unveiled

This lesson introduces students to the realm of linear equations by identifying key terms and demonstrating the process of graphing and solving these equations. It emphasizes how changes in slope and intercepts alter the function's graphical presentation, bridging the gap to practical applications.

Lesson 6. Exploring Linear Inequalities: A Comprehensive Guide

This lesson explores the relationship between linear functions through inequalities, emphasizing the importance of graphing to determine solution sets. By mastering these concepts, you'll gain a deeper insight into how inequalities operate beyond simple equations.

Lesson 7. Graphing Planes in Multiple Dimensions

By exploring systems of linear equations, Lesson 7 offers an introduction to linear algebra and substitution as a method to solve complex multi-dimensional equations. It covers graphing techniques and showcases how linear functions intersect in higher dimensions, broadening mathematical comprehension.

Lesson 8. Graphing Solutions: An Exploration of Linear Inequalities

Exploring the differences between solving systems of linear equations and inequalities, this lesson underlines the use of graphs to determine overlapping solution regions. The process is crucial for understanding linear optimization and programming, enabling learners to approach optimization problems graphically.

Lesson 9. Word Problem Solving Techniques

Through systematic approaches, this lesson enables students to handle word problems by emphasizing the importance of unit analysis and variable identification. It builds on prior algebraic knowledge to facilitate real-world application, turning abstract concepts into practical tools.

Lesson 10. Polynomials Unveiled: Understanding Their Structure and Solutions

Distinguishing between linear and polynomial functions, this lesson highlights quadratic functions as nonlinear polynomials represented by parabolas. Techniques like factoring and the quadratic formula enable the solving of quadratic equations, unraveling two potential solutions, which might be real or complex in nature.

Lesson 11. Evolving From Polynomials: Introduction to Exponential and Logarithmic Functions

This lesson covers the essential properties and applications of exponential and logarithmic functions, showing their relationship as inverse operations. Through practice problems, the lesson demonstrates how to solve equations and apply these functions in real-life contexts, such as exponential decay.

Lesson 12. Polynomial Zeros and Factorization Methods

The lesson explores the use of factoring and synthetic division to analyze polynomial functions beyond quadratics, emphasizing the importance of zeros. It demonstrates problem-solving techniques to express polynomials algebraically by their roots.

Lesson 13. Integrating Algebra into Geometry

By leveraging algebraic equations, we can extract geometric insights that would otherwise remain obscured, such as solving for dimensions given constraints. Practicing with these methods sharpens one's ability to bridge the gap between algebraic theory and geometric application.

Lesson 14. Algebra Meets Probability

Algebra serves as a key tool in this lesson to connect mathematical concepts within statistics and probability, employing variables and functions to understand random phenomena, such as multi-toss outcomes of coins. It further highlights algebra's role in deriving statistical metrics, showcasing practical applications in data analysis.

In This Course

25 Hours average completion time
2.5 CEUs
14 Lessons
29 Exams & Assignments
93 Discussions
15 Videos
14 Reference Files
Mobile Friendly
Last Updated December 2023

Description

From Basics to Brilliance: Dive into the World of Algebra

In today's fast-paced and ever-evolving world, mathematical competency is no longer a luxury -- it's a necessity. From managing household budgets to interpreting data-centric news, the importance of a solid foundation in mathematics, particularly Algebra, cannot be overemphasized. Whether you are a student setting the stage for advanced studies or an adult learner seeking to sharpen your analytical acumen, the transition from arithmetic to algebra opens doors to a world of abstract thinking and logical reasoning.

Why Algebra?
During our initial learning years, we all become familiar with the basics of arithmetic - adding, subtracting, multiplying, and dividing numbers. As we grow, the patterns of numbers beckon us to explore further, to understand not just the 'how' but also the 'why' behind mathematical operations. Enter Algebra, a branch of mathematics that goes beyond the specifics of numbers, introducing us to the exciting world of variables, constants, and their interplay. By delving into algebra, you unravel the mysteries of relationships between varying quantities, setting the stage for more advanced mathematical studies like calculus and trigonometry.

Course Overview
Our "Beginner to Intermediate Algebra" online course is tailored to guide learners through this intriguing transition. Modern data has consistently highlighted the importance of algebraic knowledge in diverse sectors, from technology to finance. Hence, understanding the crux of algebraic operations -- be it simplifying expressions, factoring complex numbers, or decoding word problems -- can enhance problem-solving abilities and set you apart in professional and academic realms.

Curriculum Breakdown:

Lesson 1: Introduction to Algebra
Unravel the world of algebra by understanding its key terms and the underlying motivation for its study. Engage in assignments that set the stage for upcoming modules.

Lesson 2: Journey Through Real Numbers
Dive into the vast ocean of real numbers. Get acquainted with their properties, classifications, and significance in the algebraic world.

Lesson 3: Mastering Algebraic Operations
From addition to division, explore how operations are transformed when we introduce variables into the mix.

Lesson 4: The Magic of Functions
Discover how functions encapsulate relationships between numbers and learn to interpret, represent, and utilize them effectively.

Lesson 5: Linear Equations & Their Graphs
Delve into the world of lines, slopes, and intercepts. Understand the foundational blocks of algebraic equations.

Lesson 6: Exploring Linear Inequalities
Not everything is equal. Learn the nuances of inequalities and their graphical representations.

Lesson 7: Systems of Equations -- Dual Interplay
When equations come in pairs or sets, there's a system. Decode methods to solve and interpret them.

Lesson 8: Systematic Inequalities
Venture into a more advanced realm where inequalities come together to form systems, providing richer insights.

Lesson 9: Word Problems -- Algebra in Action
Witness the practical application of algebra as you tackle real-world problems using mathematical tools.

Lesson 10 & 12: Diving Deep into Polynomial Functions
Understand the power and versatility of polynomials across two intensive modules, from basics to advanced applications.

Lesson 11: Exponential & Logarithmic Functions
Grasp the concepts of growth and decay, exploring natural logarithms and their applications.

Lesson 13: Geometry Meets Algebra
Experience the confluence of shapes and equations, enhancing spatial reasoning.

Lesson 14: Probability and Statistics - Predicting the World
Conclude the course by applying algebra to predict outcomes and analyze data, laying a foundation for statistical studies.

In essence, this course is not merely about learning algebra but about fostering a way of thinking. Algebra trains the mind to handle abstract concepts, solve problems, and make informed decisions. So, whether you are kickstarting your mathematical journey or rekindling an old passion, this course promises clarity, competence, and confidence. Dive in and let the numbers lead the way!

Skills You'll Develop

Applying exponential and logarithmic functions
Interpreting and utilizing functions
Exploring polynomial structures and solutions
Transforming and simplifying algebraic expressions
Applying algebra to real-world word problems
Analyzing and representing linear inequalities
Solving systems of equations and inequalities
Integrating algebra with geometry and probability
Classifying and operating with real numbers
Solving and graphing linear equations
Understanding algebraic language and significance

Skills You'll Develop

Applying exponential and logarithmic functions
Interpreting and utilizing functions
Exploring polynomial structures and solutions
Transforming and simplifying algebraic expressions
Applying algebra to real-world word problems
Analyzing and representing linear inequalities
Solving systems of equations and inequalities
Integrating algebra with geometry and probability
Classifying and operating with real numbers
Solving and graphing linear equations
Understanding algebraic language and significance

More About This Course

Master Algebraic Operations: Grasp transformation of expressions.
Boost Problem-Solving Abilities: Tackle complex tasks easily.
Explore Abstract Concepts: Understand variables and constants.
From Basics to Brilliance: Dive into Algebra effortlessly.
Algebraic Knowledge Advantage: Set apart professionally and academically.
Solidify Math Foundation: Essential for advanced studies.
Apply Math in Real Life: Solve everyday challenges effectively.
Blend Scents with Purpose: Elevate your fragrance creations.
Understand Real Numbers: Classify and utilize their properties.
Unlock Advanced Studies: Preparedness for calculus and statistics.

What You'll Achieve

Create a function using variables to determine the final cost of an item given an unspecified base price and a sales tax rate of 10%
Demonstrate an understanding of algebra by defining and providing examples of operations, variables, functions, and graphs
Demonstrate understanding of the properties of real numbers by correctly applying commutativity, associativity, distributivity, identity, and inverse in problem solving.
Identify and describe the main subsets of the set of real numbers, including natural, whole, integer, rational, and irrational numbers.
Demonstrate the ability to manipulate algebraic equalities by performing equivalent operations on both sides while maintaining equality.
Identify and apply the order of operations to evaluate algebraic expressions containing variables and parentheses.
Identify whether a given relation is a function or not by applying the vertical line test on its graph and justify the reasoning behind the result
Define and explain the concepts of domain and range of a function by providing examples and non-examples using algebraic expressions and graphical representations
Demonstrate the ability to solve linear equations and determine solutions graphically by identifying points of intersection.
Identify and describe the slope and y-intercept of a linear function given its equation in the form y = mx + b.
Demonstrate the manipulation of linear inequalities by applying appropriate rules to solve and graph solutions
Define and graph the solution set for a given linear inequality in the form ax + b > c
Recognize and describe equations in multiple dimensions by identifying expressions that represent planes in three-dimensional graphs.