# 133 Algebra Topics That Will Make You Score High

Algebra is one of those topics that gives college students a chill. The tedious calculations involved scare students to death! But do you know that there is an easy way out of all this tricky scenario? Well, on top of using algebra homework solutions, you can still try out this list of topics finely curated by math experts.

But first,

**What Is Algebra?**

It is one of the mathematics topics whereby letters and other general symbols are used to represent quantities and numbers in equations and formulae. This study majorly deals with a mathematical symbol, and there are rules involved in manipulating these symbols.

Most students find this boring and get turned off any time they have to complete an algebra assignment. The worst part comes when one has to beat a tight deadline! However, you can seek affordable math homework help and get it done with your paper in no time.

Here is a professional list of algebra research paper topics for your inspiration:

**Linear Algebra Topics**

- The essence of linear algebra in modern presentations of geometry
- How to define basic objects such as planes, rotations, and lines using linear algebra
- Discuss the interrelationship between functional analysis and linear algebra
- The application of linear algebra in the field of engineering
- Evaluate the use of linear algebra in modeling natural phenomena
- How to compute non-linear systems with linear algebra
- How does linear algebra apply in first-order approximations?
- The role of a differential of a multivariate function
- Flaws of the Gaussian elimination procedure
- The role of ancient Chinese mathematical texts in linear algebra
- Discuss the peculiarities of the systems of linear equations
- The effectiveness of using determinants in solving linear systems
- Discuss the contribution of the Theory of Extension to linear algebra

**Hot College Algebra Topics**

- The role of matrix multiplication and the inverse matrix in algebra
- How to treat a matrix as an aggregate object
- Discuss the connection between determinants and matrices
- The use of differential geometry for expression
- How does linear geometry serve in tangent spaces to manifolds?
- Discuss the electromagnetic symmetries of space-time
- What is the relationship between the history of Lorentz transformations and the history of linear algebra?
- The role of Peano introducing a precise and modern definition of a vector space
- Critique the theory of linear transformations of finite-dimensional vector spaces
- A case study of ideas and methods of calculating algebra in the 20
^{th}century

**Pre-Algebra Topics**

- Introduction to algebraic concepts: Theoretical and practical applications
- Discuss the algebraic manipulations and graphical interpretations
- An evaluation of the topics taught in middle school necessary for Honors Algebra I
- Problem-solving with inequalities and equations
- An introduction to data analysis and statistics
- Application of square roots and the Pythagorean Theorem theory
- How to use rational numbers and their application in algebra
- A look at expressions, variables, and arithmetic review
- Translating between math and words in algebra
- Adding and subtracting mixed numbers and fractions

**Researchable Topics in Algebra**

- A review on using the order of expressions in algebra
- Analyze the use of the absolute value of integers
- Considerations when dividing and multiplying fractions.
- How to translate between expressions and tables in algebra
- Simple ways of solving equations containing decimals and fractions
- How to write and solve two-step equations like an expert
- Discuss the quotient properties of exponents when solving algebraic equations
- A case study of the scientific notation in the application of exponents
- What is the difference between rational and irrational numbers in algebra?
- How to solve algebraic equations with variables on both sides

**Impressive Topics in Linear Algebra**

- Easy ways of solving algebraic ratios and unit rates
- Difficulties students encounter in solving percentage increase and decrease
- How to estimate with algebraic percentages
- A case study of quadrilaterals, polygons, and triangles in algebra
- The role of volume and surface area of spheres in algebraic equations
- How to solve problems dealing with angles formed by transversals
- Solving the circumference and area of a circle using algebra
- Difficulties encountered in using bar graphs and histograms
- How to work with the Box-and-Whisker plots
- Challenges involved in collecting, organizing, and interpreting algebraic data

**Intermediate Algebra Topics**

- Discuss the procedure of translating word problems from English to math
- How to work with graphing systems of linear inequalities
- The role of the quadratic formula in simplifying algebraic problems
- Special factoring formulas: A case study of the sum of cubes and difference of squares
- How to solve systems of non-linear equations
- Discuss the three types of variation: Inverse, joint, and direct variations
- How to work with the rotational roots test
- How to find polynomials from their zeroes
- Painstaking ways of handling quadratic word problems
- How to work with the absolute-value inequalities

**Amazing Algebra Topics List**

- How to graph absolute value equations in algebraic problems
- What is the role of the x and y-intercepts in an algebraic equation?
- Determine how you can solve the slope of a straight line
- Simplifying with parentheses: The pros and cons
- How to convert between percent, fractions, and decimals
- Evaluate number properties: A case of associative, distributive, and commutative properties
- Dealing with number bases: A case analysis of octal and binary number bases
- Why should you bother taking algebra at any school level?
- The basic rules of solving exponent algebraic equations
- Discuss the order of operation with a special emphasis on BODMAS

**Top Algebra Topics High School**

- A look at the overview and history of algebra
- Examine the problems encountered in solving two-linear equations
- An introduction to slope-interception
- How to recognize and differentiate various functions in algebra
- What are the requirements for determining the average rate of change?
- Solving absolute value and piecewise functions
- The role of exponents and radicals in Algebra I
- Discuss how to solve exponential growth and decay using algebra
- Strategies in dealing with monomials and binomials
- Why most students prefer the vertex form of quadratic equations

**Advanced Algebra Topics**

- Handling complex fractions in algebra
- How to define and simplify rational expressions
- The role of rational graphing functions in algebraic equations
- How to easily multiply rational expressions using modern formulae
- Log rules involved in solving logarithms and log equations
- Discuss the different systems of linear equations applied in algebra
- Matrix row operations that can help you solve a complex algebraic problem
- Determinant word problems and how to tackle them
- An overview of conics: A case of parabolas, circles, ellipses, and hyperbolas
- How to type math assignments when posting questions on tutoring forums or e-mailing to a lecturer

**Abstract Algebra Topics**

- A study of the rules for manipulating formulae and algebraic expressions
- Discuss the algebraic structure: A case of sub-modules, sub-groups, and sub-rings
- Discuss the closure of a binary operation process
- The role of the additive inverse, multiplicative inverse, and inverse element in a unary operator
- How to use kernels and cokernels in homomorphism
- Evaluate quotient objects: A case study of quotient ring, quotient group, and quotient module
- What are the different categories of the abelian groups?
- Discuss the classification of finite simple groups in algebra
- Discuss the process of presenting a word problem for groups
- Finitely generated abelian group: A case study of the types

**Manageable Topics in College Algebra**

- How to sketch graphs of the basic functions in algebra
- The role of vertical shifts in graphing functions
- How to form and evaluate composite functions in algebra
- How to determine whether a function is one-to-one using the horizontal test
- Discuss the process of finding the inverse of a one-to-one function
- How to graph a quadratic function written in vertex form
- How can you determine the equation of a quadratic function given its graph?
- How to maximize the projectile motion functions
- Discuss the process of sketching the graph of power functions
- Determine the possible equation of a polynomial function given its graph

**Advanced Topics in Algebra And Geometry**

- How to evaluate logarithmic expressions
- Discuss the different properties of exponential functions
- How to plot ordered pairs in the rectangular coordinate system
- How to convert the general form of a circle into a standard form
- How to find the midpoint of a line segment
- Calculating the distance between two points using the distance formula
- How to solve the three-part inequalities
- How to solve linear equations involving decimals
- Using single radicals to solve equations
- The role of the discriminant in determining the type of solutions for a quadratic problem

**Quality Project Topics in Linear Algebra**

- How to solve three-part inequalities
- Simplifying linear algebra equations
- Variables and expressions
- Arithmetic operations of integers
- Equivalent fractions in linear algebra
- Two-step inequalities
- Proportional relationships
- Direct variation
- Rational equations
- Linear equations involving decimals

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