Prologue Before we begin, take a second. Open this link in a new tab. Did you do it? I’ll wait. Oh, you opened it? Great. Sorry for the forwardness, but this book is one of the greatest tools I have used in taking myself from a beginner in programming to a full time data scientist.Continue reading “A Guide to Probability With Biological Data: Topics of Data Modeling”

# Category Archives: Mathematics

## The Correlation Coefficient with Biological Data: Topics of Data Modeling

Introduction to the Correlation Coefficient Our discussion in this series on data modeling focuses on statistical tools which function to statistically represent biological data. The initial articles gave an initial foray into the topic, addressing the uses of statistics and a bit of insight into the concept of sampling. Following this, we expanded upon the generalContinue reading “The Correlation Coefficient with Biological Data: Topics of Data Modeling”

## The Lemmas of Linear Combination: Topics in Linear Algebra

Introduction To The Lemmas of Linear Combination The present endeavor of this series on linear algebra centers around the essential computations associated with linear systems. This common thread unifies all topics pertaining to this subject. Our first article began elaborating on the primary methodology of deriving the solution for a linear system, the Gaussian method.Continue reading “The Lemmas of Linear Combination: Topics in Linear Algebra”

## A Guide to Gaussian Jordan Reduction: Topics in Linear Algebra

Introduction to Gaussian Jordan Reduction This series regarding linear algebra has focused primarily on subject matters relating to facilitating understanding of linear systems. In our first article of this series, we elaborated in great depth on explicating the Gaussian method as it exists as a technique for solving linear systems. This article was immediately followedContinue reading “A Guide to Gaussian Jordan Reduction: Topics in Linear Algebra”

## A Guide to Estimations with Biological Data: Topics of Data Modeling

Introduction to Estimations with Biological Data Our series on modeling biological data has elaborated on a variety of statistical concepts. The initial articles gave an initial foray into the topic, addressing the uses of statistics and a bit of insight into the concept of sampling. Following this, we expanded upon the general array of different types ofContinue reading “A Guide to Estimations with Biological Data: Topics of Data Modeling”

## Descriptive Statistics with Biological Data: Topics of Machine Learning

Introduction to Descriptive Statistics with Biological Data Our series on statistical data modeling has emerged from it’s introductory era into something with a bit more substance. Our initial articles gave an initial foray into the topic, addressing the uses of statistics and a bit of insight into the concept of sampling. Following this, we expandedContinue reading “Descriptive Statistics with Biological Data: Topics of Machine Learning”

## How to Use Directional Derivatives For Machine Learning: Topics of Partial Derivatives

Introduction By this point in our series on partial derivates, we not only have expanded upon the idea of multivariate equations, but also introduced the taking of partial derivatives and their associated tangent planes/linear approximations. If you have not referenced these items, we highly recommend it, for as we proceed in our application of theseContinue reading “How to Use Directional Derivatives For Machine Learning: Topics of Partial Derivatives”

## Guide to Tangent Planes and Linear Approximation: Topics of Partial Derivatives

Overview Up to this point, we have really highlighted the nuts and bolts of working with partial derivatives. Firstly, it began by elaborating the roles of equations comprised of multiple variables. We extrapolate on those insights in this article. Secondly, we took a brief detour to examine the nuances of limits and continuity in theseContinue reading “Guide to Tangent Planes and Linear Approximation: Topics of Partial Derivatives”

## A Guide to Partial Derivatives: Topics of Partial Derivatives

Setting the Ground on Partial Derivatives Our series which elaborates on the topic of partial derivatives began first by introducing functions of multiple variables. An understanding of how these functions operate is integral to executing partial derivatives. If you need a refresher on this subject before embarking further, check out this article. Furthermore, limits areContinue reading “A Guide to Partial Derivatives: Topics of Partial Derivatives”

## Limits and Continuity Multi-Variable Functions: Topics of Partial Derivatives

Overview of Functions With Multiple Variables If you’ve been following in our blog, you may have found our discussion of vector calculus before arriving here. If not, it may prove useful to start with this topic; you may find it here. Nevertheless, limits and continuity are fundamental to conceptualizing the various aspects of calculus, andContinue reading “Limits and Continuity Multi-Variable Functions: Topics of Partial Derivatives”

## Modeling Functions of Multiple Variables: Topics of Partial Derivatives

Introduction to Functions of Multiple Variables Prior to now, we have quite frequently worked with functions that relate a single variable to another variable. These functions tend to take the form: Here, f(x) represents the traditional variable y. However, in this article, we investigate higher functions that rely on relationships between multiple variable inputs. WeContinue reading “Modeling Functions of Multiple Variables: Topics of Partial Derivatives”

## Methods of Biological Data Modeling: Techniques of Statistical Display

Modeling Biological Data Statistics is the cornerstone of science. Data serves as the matter by which statistics operates upon. However, these numerical computations are seldom useful unless they are efficaciously modeled. The purpose of data modeling is to organize data and statistical information in a succinct form such that observation of the model itself providesContinue reading “Methods of Biological Data Modeling: Techniques of Statistical Display”

## A Guide to Modeling Biological Data: Introductory Statistics and Sampling

The Premise When it comes to working with biological systems, a prolific amount of data may be generated. Whether it be working with an animal population, modeling protein interactions, or accessing gene identities, biological systems are hot beds for data. This data is useless unless we have some way to understand it. This modeling biologicalContinue reading “A Guide to Modeling Biological Data: Introductory Statistics and Sampling”

## How to Describe the Solutions of Linear Systems: Linear Algebra

What is a Solution Set? When it comes to operations on linear systems, the purpose of our efforts are often motivated by a need to solve the system. For this to be true, we must identify a solution. The solutions of a linear systems denote the values which when substituted into the equation, returns aContinue reading “How to Describe the Solutions of Linear Systems: Linear Algebra”

## Gaussian Method of Solving Linear Systems: Linear Algebra

Introducing the Gaussian Method and Linear Algebra Linear algebra is a subject devoted to understanding complex equations that interact together to form systems. The Gaussian method is the premise of linear algebra, and provides tools which help discern the solution of a linear system. The Gaussian method is an algorithm of steps which constitutes meaningfulContinue reading “Gaussian Method of Solving Linear Systems: Linear Algebra”

## Arc Length and Curvature: Computations for Vector Calculus

The Arc Length and Curvature Question Computing the arc length and curvature of various functions is one of the principal applications of the vectorial calculus we have just learned. Our first article provided a broad introduction into the world of calculus. The subsequent article takes time investigating the dot product and cross product in depth.Continue reading “Arc Length and Curvature: Computations for Vector Calculus”

## Vector Differentiation and Vector Integration: Vector Calculus

Vector Differentiation and Integration: An Intro Vector functions can be readily subjected to computations of differentiation and integration in order to derive different components of space curves. Our first article on the subject of vector calculus laid out the various aspects of vector calculus. This included a review on vectors, examination of certain types ofContinue reading “Vector Differentiation and Vector Integration: Vector Calculus”

## Vector Functions and Their Uses: Graphing and Applications

Vector Functions: The Scoop If you read our previous post on vector calculus, you likely observed an extensive documentation of topics within the subject. And if you arrived here having just explored our post on dot products and cross products, then you are already aware of the useful computations associated with vectors. However, these computationsContinue reading “Vector Functions and Their Uses: Graphing and Applications”

## Cross Product and Dot Product Computation : Vector Calculations

Cross Product and Dot Product Our previous article discussing nuances of vector calculus presented features of the dot product and cross product. These vector computations, though not too complex, are nevertheless fundamental to performing higher level methods. This article provides proofs for these functions to foment comprehension of their governing dynamics. Furthermore, we analyze severalContinue reading “Cross Product and Dot Product Computation : Vector Calculations”

## Stuck On Vector Calculus? We Got You Covered.

The word ‘calculus’ itself is sufficient to make the average person cower away, let alone attaching obscure adjectives to such a terrifying concept. Nevertheless, vector calculus opens the portal to a much higher of mathematical computation, and for those in specialized fields, has a wide range of applications. This post serves to provide some clarityContinue reading “Stuck On Vector Calculus? We Got You Covered.”