#Mathematical Expectation and Generating Function Assignment Help

[lipshits-continuous]

Topological Spaces 1: Introduction and Metric Spaces

Welcome to the first of several posts about general topology! The goal of these posts is to give an overview and introduction to key concepts in topology. I will try to give intuitions about definitions and results so that even if you're not as aquainted with formal mathematics you can still get something from this. Whilst there aren't any prerequisties per say (for the reason above), for those who are interested in the moral formal aspects it will be helpful to be familiar with real analysis. Some familiarity with linear algebra is also helpful in this post though probably won't play a role going forward.

Topology is such a broad subject that assigning one goal is quite hard. One early goal is to generalise the notion of continuity and other familiar notions, which we shall do. Topology certainly doesn't stop there. One large goal is to find properties which are invariant under homeomorphism (bijective continuous maps whose inverse is also continuous). We shall see some examples of this as we go further!

The goal of this post is to give context to the definitions of topological spaces and continuity via the study of metric spaces. The definition of a topological space can seem quite dry and like it's been plucked out of thin air when just presented without motivation. In this sense, metric spaces are the bridge between familiar concepts in real analysis and the more general setting of topology.

1.1: Metric Spaces:

As the name might suggest, metric spaces are sets with an appropriate notion of distance between points in the set. For the real numbers, we have an intuitive sense of distance between two numbers: the absolute value of their difference. From this, we can immediately get three desirable properties we'd want a notion of distance to have:

Positivity: |x-y|≥0

|x-y|=0 if and only if x=y

Symmetry: |x-y|=|y-x|.

These are desirable because this says, in order, that distance is always positive, two points are the same only when the distance between then is 0, and the distance beween x and y is the same as the distance between y and x.

The last property is not as immediately obvious from the definition but is still a fairly intuitive property that we'd expect a notion of distance to have: the triangle inequality. Formally, for any x,y, and z real number we have |x-y|≤|x-z|+|z-y|. This just says that the distance between two points is always shorter than the distance achieved by adding an intermediate point. The name comes from visiualising this with lengths of a triangle! The proof that this holds for the absolute value can be found here.

You might ask whether there are any more properties we'd like but it turns out that this is enough to generalise a lot of concepts in real analysis in an appropriate way. That is, we still maintain a lot of nice results without requiring too many rules. So let us finally see the definition!

Definition 1.1:

Note: It's common to combine the first two axioms together but for the sake of clarity, I have separated them.

Examples 1.2:

The details of why each of these is a metric can be found in this post.

A result of the second example is that metric spaces are also an appropriate generalisation of normed vector spaces. The fact they are a generalisation is seen from the fact that the discrete metric cannot be seen as the result of a norm and isn't restricted to vector spaces.

1.2: Continuity:

Intuitively, continuous functions are ones that don't have gaps or sudden jumps. In the case of functions from the real numbers to itself, we can view this as "we can draw its graph without lifting the pencil". This can be restated as "points that are close to each other remain close to each other after the function is applied". But how does one formalise "closeness"? With distances of course!

Definition 1.3:

Remark: Continuity departs on the metrics. A function that is continuous in one metric isn't necessarily continuous in another.

Examples 1.4:

Now I'd like to prove a fairly common result to further demonstrate continuity.

Proposition 1.5:

1.3: Open Sets in Metric Spaces

Now we shall see the first aspects of topology creeping in. One way to think about open sets which don't have any points "at the edge". This is immediately clear in the definition we will give below but when we generalise the notion of an open set, we will seemingly lose this. However, we will see that this intuition will still hold!

Definition 1.6:

Example 1.7:

We will now define the notion of an open set using these open balls.

Definition 1.8:

This does indeed formalise "no points at the edge" since for open sets, all points close enough to x are always in U.

Remark: Openness depends on the metric. For example, {0} is open in the real numbers with the discrete metric but not with the absolute value metric.

Now, "open ball" would be a silly name for it if they weren't indeed open in the sense of definition 1.8 but luckily they are!

Proposition 1.9:

Example 1.10:

Open intervals of real numbers are indeed open with respect to the absolute value. If we have the open interval I=(a,b) for finite a<b, we may view I as an open ball by setting x=(b+a)/2 and r=|b-a|/2. Then I=B(x;r).

Now we shall prove a very important result about open sets that lets you build new open sets out of old opens but will also be the foundation upon which we generalise the notion of open sets!

Lemma 1.11:

Proof:

Remark: Finiteness is important for 3. If we consider the real numbers with the absolute value metric then (-1/n,1/n) is open for all (non-zero) natural numbers. However their intersection over all n is {0} which is not open in this metric.

Typically, courses would usually talk about closed sets now. However, since the discussion doesn't vary much between metric spaces and topological spaces, we will hold off for now.

1.4: Continuity in terms of open sets

This is a very important step in our journey in generalising continuity. This section with along with the next section will suggest that open sets are actually the structures we'd like to study!

Lemma 1.12:

Before we prove this, I'd like to just comment on why this still alligns with our intution about continuity. The right hand side is saying that points end up close together in Y must've been close together in X.

Remark: It is important to note that U open in X does not necessarily imply f(U) is open in Y when f if continuous. For example, take f(x)=x² in ℝ with its usual notion of continuity, then (-1,1) is open but f((-1,1))=[0,1) which is not open. Maps for which open sets are mapped to open sets are called open maps.

We will see examples of how to use the property on the right hand side in the next post!

1.5: Equivalent Metrics

The goal of this section is to see that sometimes different metrics will give rise to the same open sets!

Definition 1.13:

Example 1.14:

I will omit the details of the proof for brievity. Not that the 2 on the right hand side comes from the fact we're in ℝ² and isn't related to the 2 in the metric.

Remark: Not all metrics are equivalent. The discrete metric and d₂ are not equivalent metrics.

Proposition 1.15:

Corollary 1.16:

This ultimately means that some metrics generate the same open sets. Then Lemma 1.12 tells us that equivalent metrics give the same continuous funcitons since we can view continuity in terms of open sets. This suggests that what really matters here is which sets are open. This is what we shall exploit to generalise continuity even further! But that shall have to wait til the next post!

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Time Management Strategies for CDS Exam Preparation

It can be challenging, but it will also be rewarding, preparing for the Combined Defence Services (CDS) exam. Proper and scientific time management is the prime requirement for success. Once that time is managed well, achieving a balance between study schedules and other commitments becomes quite easy. 

In this blog, a number of effective strategies for time Management for CDS exam are discussed, which will allow you to maximize study time by improving your performance.

1. Understand the CDS Exam Pattern

It would be wise to learn about the functioning of the CDS exams before charting your study plan. The whole examination is further divided into three papers: English, General Knowledge, and Mathematics. Each has a different number of questions and time allotted to answer it. Knowing how each section is structured and weighed will enlighten your study schedule. This way, you know what to expect and can prepare for the examination thoroughly covering all subjects with your studies.

2. Create a Realistic Study Schedule

Building a precise timetable for studying is important in managing time management for CDS exam. Use your study material to break it down into elements and assign a particular time frame to each of the elements. The following may help create your timetable:

Set Achievable Targets: Make small realistic targets to be achieved daily and also some weekly so as to boost and motivate you.

Prioritize Topics: Spend most of the time on a topic difficult than short the other areas.

Include Breaks: Take short breaks between the sessions of studying, refreshing your brain and improving concentration.

Follow the nicely laid study schedule, and you can easily cover almost all important areas of the syllabus.

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Time Management Strategies for CDS Exam Preparation

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Caktus AI Overview: Features, Usage, Tips, and Limitations

The influence of AI extends across numerous fields, including education. One notable tool in this domain is Caktus AI, an all-encompassing AI educational platform designed to meet the needs of both students and educators. This tool is equipped with various features, such as writing code, essays, paragraphs, and solving mathematical problems.

In this article, we explore the functionalities of Caktus AI, provide a usage guide, offer suggestions for optimizing its use, and highlight its limitations.

Introducing Caktus AI

Caktus AI is an advanced educational platform leveraging AI to assist students, instructors, and professionals in their academic and career pursuits. Its features include essay writing, math problem solving, paragraph generation, discussion question creation, personal statement crafting, and a unique YouTube to essay tool.

The platform also offers text summarization, coding tools for languages like Python, Java, C#, JavaScript, and Go, and a career section for building cover letters and resumes.

Key Features of Caktus AI

Writing Aid

Essays: Caktus AI helps users craft essays on various topics. By providing a prompt, users receive a well-structured essay with appropriate citations. The tool also offers a content-improver feature to refine grammar, tone, and style.

Paragraphs: The Paragraph Generator creates original content based on a brief description, delivering a coherent paragraph in 15-30 seconds.

Personal Statements: For college or university applications, the personal statement writer analyzes users' skills and achievements to produce personalized statements.

Resume Bullet Points: Caktus AI generates structured resumes highlighting users' skills, experiences, and achievements, with options to save and export in multiple formats.

Blog Posts: The platform assists in creating blog posts on various topics, ensuring well-researched and informative content.

Love Letters and Songs: Users can generate love letters and songs, customizing the output for a personal touch.

Coding Companion

Caktus AI supports code generation in multiple programming languages, making coding more efficient for both beginners and experts. Users can generate unique code, access a code editor and debugger, and receive suggestions for code improvement.

Language Learning Tool

The platform aids in learning languages like Spanish, Russian, Japanese, French, Arabic, Mandarin, and Italian. Users can improve pronunciation, grammar, and cultural understanding, and translate text between languages.

Learning Aid

Caktus AI offers various tools to enhance learning and teaching efficiency:

Automated Grading: Streamline evaluations, provide feedback, and track student progress.

Personalized Learning: Create tailored learning experiences and track student progress.

Time Management: Track assignments, set reminders, and manage study schedules.

Flashcards: Create and share multimedia flashcards for collaborative studying.

Math Solver: Quickly solve equations and mathematical problems.

Using Caktus AI

To use Caktus AI, users must sign up for an account and choose a subscription plan ($4.99/month or $39.99/year). After registration, users can select features like the AI paragraph generator, essay writing, or coding tools. By providing a prompt, the platform generates the desired content.

Tips for Maximizing Caktus AI's Potential

Be Precise: Frame inquiries concisely to receive accurate responses.

Provide Context: Offer relevant details for tailored answers.

Stay Open-Minded: Understand that AI may not always meet expectations but can provide valuable insights.

Ask Follow-Up Questions: Delve deeper into topics for a better understanding.

Supplement Learning: Use Caktus AI as an aid alongside other educational resources.

Caktus AI Limitations

While Caktus AI's essay writer can quickly generate various text formats, reliance on this feature may border on academic dishonesty. Users should fact-check and validate the content, as errors may occur. Additionally, the platform lacks clear support/contact information and may not always generate output swiftly.

Caktus AI vs. ChatGPT

Caktus AI: Specializes in educational tools for students and educators, offering a personalized experience at a lower cost ($4.99/month).

ChatGPT: Provides more human-like conversations and is suitable for general purposes. ChatGPT offers a free version, unlike Caktus AI.

FAQs

Pricing: Caktus AI costs $4.99/month or $39.99/year, with automatic renewal.

Beneficiaries: Ideal for students, educators, and job seekers.

Privacy: Ensures user data is encrypted and securely stored, with no third-party sharing without consent.

Conclusion

Exploring AI's capabilities, Caktus AI stands out as a versatile tool that enhances productivity, creativity, and learning across various domains. Whether you're a student, educator, or professional, Caktus AI provides the tools needed for success.

[eintsein]

hi hi! could you please share your study techniques and advice for economics majors? I survived lower division just fine but upper division courses :( .

Hii! First of all, I want to apologize for answering this quite late - I wanted to give you an answer that's thorough enough and helpful. Read on below for tips!

Disclaimer: these tips are from my own experience and the experience of my peers, most of whom are in US institutions. However, I do think these tips should apply to many economics major programs.

Strengthen your mathematics foundations

Upper-division economics courses are math at their core. Here's an example of the objectives of an intermediate microeconomics course (source)

understanding the concepts of Pareto and sum-of-surplus efficiency, being able to determine whether a preference relation is complete, transitive, monotonic, and convex, and being able to determine whether a production function exhibits increasing, decreasing, or constant returns to scale.

Preference relations are concepts from discrete math. Increasing, decreasing, and constant returns are concepts from calculus.

Many upper-division courses also require knowledge of probability and statistics (game theory courses especially). Research-based classes often recommend having taken econometrics. Theoretical classes like decision theory are, as the name suggests, theoretically rigorous, so being comfortable with proofs is necessary, and knowing math theory is a great help.

A lot of people (myself included) struggle with higher division economics courses because they were not mathematically prepared. While you can definitely learn as you go, it will make your life a whole lot easier having the preparation or at least the comfort to work with the required mathematical concepts and use certain mathematical skills.

An example from personal experience: I had taken econometrics (a theoretical version) the spring of my sophomore year without much knowledge of multivariable calculus and having taken calculus II over a year before taking this class, and honestly I felt I had to work so much harder than my peers who were math majors or minors.

So yeah, you should definitely brush up on your math skills if you find yourself struggling. This could mean doing extra practice, looking for tutoring, or even taking a course.

Strengthen your economics foundations

Upper-division economics courses really build on lower-division courses. As far as I know, the purpose of upper-division courses is to teach us to synthesize what we learned from lower-division courses, i.e. to use the tools and techniques we've learned, and apply them to new economic settings.

For example, last fall I took a course on public finance (also known as welfare economics) and one of the topics we studied was regulating pollution. Two of the regulation methods we focused on were 1) cap & trade, i.e. giving pollution permits that can be traded, and 2) emission fees, i.e. setting a fee if emission is above a certain amount. The graphs below illustrate the two methods for two cases: inelastic marginal social benefit of pollution reduction, and elastic MSB of pollution reduction. Marginal cost and marginal social benefit curves are usually taught in lower-division courses, as are concepts of elasticity and demand-supply models.

Another example from the same class: evaluating Pareto efficiency of the allocation of public goods involves being comfortable with indifference curves, utility functions, and production possibility curves, as shown below. (Even if you don't understand what's going on, the general shapes should look familiar.)

Use the course's learning objectives to guide you

My probability and statistics professor taught me that the first step in studying any subject is to look at the learning objectives. These are the things you are expected to get out of the course and so they are the things you will be expected to know on an exam, do in a project/assignment, etc., not just information but also skills and techniques.

Study and practice drawing graphs

Graphs can hold a lot of information given that you know how to interpret them. In many cases, I found that if I understand the graph, then I understand the concept. Studying graphs saves a lot of study time, too, since the material's been summarized really neatly, and chances are you'll need to know the graph, too.

For many of my economics classes, I create a study guide comprising only graphs. These aren't just the graphs that are explicitly taught in class, though. I try to include as many cases, including special cases, because it teaches me to be able to think through the concepts being used in the graphs, instead of just being like, okay this is what it looks like.

For example, when studying Edgeworth-Bowley boxes, I drew them with different types of indifference curves, and then for each of them, I drew their utility possibility frontiers. Or when studying anything involving demand-supply curves (e.g. different types of taxation), I draw a graph for each combination of demand and supply elasticities (e.g. inelastic demand with inelastic supply; inelastic demand with elastic supply; etc.).

Of course, I don't always get it right. If there's something I'm unsure about or don't understand, I go to office hours for help.

Learn from assignments and practice a lot

Your assignments point out the types of questions you'll be expected to analyze and work through and thus can guide your studying, whether it's mathematical problem sets or a series of essays.

In classes with problem sets, doing them seriously helps SO much. They train your mental muscles to be able to solve or analyze the problems you're expected to be able to solve and analyze after taking the course. Your professor created these problem sets to achieve the learning objectives. If you're having trouble with any part of the problem set, you probably don't understand a key concept, skill, or technique the course expects you to, and that's totally fine; just don't forget to work on it and ask for help.

In addition, problem sets also serve as great revision tools to help you actively recall and synthesize the material you've studied.

Go to office hours for conceptual help

I've mentioned a couple times to reach out for help if you need it and I cannot stress this enough. In most cases, professors and TAs (teaching assistants) are more than willing to help you succeed. I would suggest going to each instructor/staff member if there are multiple and seeing which one is the most helpful, i.e. the person who can fill in your knowledge gaps the easiest, who understands your misunderstandings. Sometimes it's the professor, other times the TA is a better fit. Sometimes the TA gives better help for problem sets but the professor gives better help for conceptual problems. Use the resources available to you!

I hope this helps, and please don't hesitate to reach out if you have any other questions :)

[lovemyvidcode]

5 Projects for Computer Class

Computer class can and should be more than just the basics of typing and the understanding of how to use web applications. Computer class should be fun. Why? Because when your students are engaged, they’re learning. And that’s what it’s all about.

We’re going to go over five fun projects to use in your computer class. Not only are these activities engaging, they’re cross-curricular, and meet Common Core, AP, and Computer Science standards. Better yet? They include strategies to build communication and critical thinking skills.

Projects we’ll go over in this article are:

Create a Filter

Make a Meme

Bestie Greeting Card

Code the News

Climate Clock

Let’s get to it!

Create a Filter

Using the basics of JavaScript, your students will create fun, unique filters for videos that reflect their abilities and personalities. They can use the videos provided by Vidcode, or they can use videos of themselves. Sign up to assign Create a Filter to your class, or visit vidcode.com/project/filters.

Reflection Questions

Who is a programmer?

What is a function?

What is an argument?

Standards Addressed

CCSS.MATH.PRACTICE.MP7 Look for and make use of structure.

NGSS Practice 5 Using mathematics and computational thinking

CSTA 1B-AP-11 Decompose (break down) problems into smaller, manageable subproblems to facilitate the program development process.

CSTA 1B-AP-15 Test and debug (identify and fix errors) a program or algorithm to ensure it runs as intended.

Make a Meme

Memes have changed the way we communicate - often with a sense of humor. This is a project your students will love! Your students will use JavaScript to embellish a video with graphics and text. Sign up to assign Create a Filter to your class, or visit vidcode.com/project/graphics.

Reflection Questions

What is a project?

What is a method?

Standards Addressed

CCSS.MATH.PRACTICE.MP6 Attend to precision.

CSTA 1B-AP-09 Create programs that use variables to store and modify data.

CSTA 1B-AP-11 Decompose (break down) problems into smaller, manageable subproblems to facilitate the program development process.

CSTA 1B-AP-14 Observe intellectual property rights and give appropriate attribution when creating or remixing programs.

CSTA 1B-AP-15 Test and debug (identify and fix errors) a program or algorithm to ensure it runs as intended.

Bestie Greeting Card

Help your students spread the love by creating a greeting card!

This is a special hour of code project. Using JavaScript, your students will create a greeting card while learning about pixels and placing them on an  x-y grid, using and writing functions, and changing function values to create different effects. Use Bestie Greeting Card with your class.

Reflection Questions

How would you explain creative coding to a friend?

What did you learn during this hour of code?

Standards Addressed

CSTA 1B-AP-09 Create programs that use variables to store and modify data.

CSTA 1B-AP-10 Create programs that include sequences, events, loops, and conditionals.

CSTA 1B-AP-15 Test and debug (identify and fix errors) a program or algorithm to ensure it runs as intended.

CSTA 1B-IC-21 Use public domain or creative commons media, and refrain from copying or using material created by others without permission.

CSTA 1B-IC-18 Discuss computing technologies that have changed the world, and express how those technologies influence, and are influenced by, cultural practices.

Code the News

In this Hour of Code projects, students follow the provided tutorial that walks them through the basics of JavaScript, functions, and other programming basics.

In this project, we offer extension activities beyond just the hour of code, allowing students to dive deeper into the meanings of conditionals and functions. During the activity, students are encouraged to explain their thinking to their classmates using small-group and whole-group discussion questions. Use Code the News with your class.

Reflection Questions

Does code look like you expected? Is it easier/harder?

What is a function?

What is an argument?

Are you impressed your code is looking more advanced?

Standards Addressed (a handful, because so many are addressed across the curriculum!) Common Core Standards for Mathematical Practice

CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.

CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively.

CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others.

Next Generation Science Standards for Engineering Practices

Practice 1 Defining problems

Practice 2 Developing and using models

Practice 3 Planning and carrying out investigations

CSTA

CT.L2-01 - Use the basic steps in algorithmic problem-solving to design solutions (e.g., problem statement and exploration, examination of sample instances, design, implementing a solution, testing, evaluation).

CT.L2-03 - Define an algorithm as a sequence of instructions that can be processed by a computer.

CT.L2-04 - Evaluate ways that different algorithms may be used to solve the same problem.

CT.L2-07 - Represent data in a variety of ways including text, sounds, pictures, and numbers.

Climate Clock

Give your students the chance to use programming to change the world. In this Climate Clock project, students address the climate crisis.

Climate Clocks give a visual representation of just how urgent the climate crisis is. In this project students will create their own climate clocks. Your students will use JavaScript’s Date object to keep track of years, months, days, hours, seconds, and even milliseconds.

Students will also be introduced to modulo, the important math behind keeping the units used in the code straight. Use Climate Clock with your class.

Reflection Questions

What is some other information that you think would be useful in a Climate Clock?

What else do you think is important to keep track of?

How can engaging in work like this make a difference?

Standards Addressed

CSTA 3-5.AP.08 Compare and refine multiple algorithms for the same task and determine which is the most appropriate.

CSTA 6-8.AP.11 Create clearly named variables that store data, and perform operations on their contents.

CSTA 6-8.AP.13 Decompose problems and subproblems into parts to facilitate the design, implementation, and review of programs.

CSTA 6-8.AP.16 Incorporate existing code, media, and libraries into original programs, and give attribution.

Conclusion

Your students are the future of coding and programming. They deserve awesome instructors like you to facilitate learning experiences that are applicable to real life. Thankfully, Vidcode has made this easier for everyone by offering these five fun and engaging coding projects for your students. These five programming projects cover cross-curricular standards, supported by critical thinking discussion prompts. These projects will introduce important coding skills to your students as they get a taste for how their coding abilities can impact the world around them.

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Mathematical Expectation And Generating Function Homework Help

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Mathematical Function Assignment Help| Mathematical Function Online Help| Mathematical Function  Homework tutors Help

Students can access our Mathematical  Expectation and Generating Function homework assistance by contacting us  through our website where a student can submit an assignment. Alternatively, Mathematical   Expectation and Generating Function homework experts can be contacted through  our email id statisticshomeworktutors@gmail.com .Our  college professional Mathematical Expectation and Generating Function serve  students globally; this has positioned them to tackle different Mathematical  Expectation and Generating Functions problems hence boosting their experience.  

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Mathematical Expectation and Generating Function Assignment Help

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Mathematical Expectation and  Generating Function is a key area of study often encountered by scholars pursuing statistics and mathematics courses. The Mathematical and Generating Function course has over  the years presented problems to students bearing Mathematical Expectation and  Generating Function homework. The complexity of the Mathematical Expectation  and Generating Functions course lead to the need for us to establish Mathematical  Expectation and Generating Function homework help services. This Mathematical  Expectation and Generating Function help tutors are mandated with the task of   completing all Mathematical Expectation and Generating Function assignments.  There are a number of services offered by online Mathematical Expectation and  Generating Function help department, they include completion of all troublesome  Mathematical Expectation and Generating Function repots, dissertation,  completing calculation and offer online Mathematical Expectation and Generating  Function online tutoring.

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lunarcanine reblogged your post and added:

I never had it as terrible as that, however, I can relate to that. I use ‘big words’ that my classmates always tease me about, and I talk about psychology and disorders and syndromes when I can, and drop in facts when the opportunity is given. My main source of positivity was from the praise, and the only reason I have friends is because my extrovert father has an extremely high social expectation so I just….made friends that I have to this day. I still long for someone who can be as weird as me. And literally every adult I have a conversation with says something like ‘woah you sure are genius! How does she know all of these things?’ and I just think that they hold very low expectations for childrens. I just know a lot.

I took an IQ test when I was younger, five or six….and I think I got average. So even being average, I can relate to thse things

Okay, I’m gonna babble at you a little about the brain.

What we’re really talking about, at its base, is neurodivergence. It’s the idea that on whatever measure of brain functioning, the vast swath of humanity fits into one general model, and outliers are very rare. 

To compare brains to physical bodies: Most humans have ten fingers and ten toes. I, for some obscure reason doctors don’t know, was born with eight fingers and nine toes. I’m a little off the standard expected model physically. About 1 in 50 babies is born with some sort of congenital abnormality like that.

So, to brains: A neurodivergent brain is one which, in some measure, is a little different from the expected “neurotypical” brain. This can be in a few small isolated areas, or over a broad number of different areas of the brain. 

Because your brain has a lot of different systems that can function really differently--language is in a different location than mathematics, those are in a different place than music, which is different from physical coordination, which is different from the ability to pay attention, which is different from your ability to understand and empathize with other people, which is different from how emotional you get or how much you can control those emotions. These systems can all work together, but we also have an amazing ability to separate them--so you can read and walk at the same time, or cook dinner and write a story in your head. And they can be affected differently--someone can be neurodivergent primarily in one of these areas, or they can be neurodivergent in a lot of them.

When someone’s brain is different enough from the neurotypical model to cause distress or impairment relative to other people, that difference is usually given a diagnostic label and categorized as a mental illness or learning impairment. When these differences are seen as positive, they’re rarely studied, just kind of generally glossed as “gifts” and “talents” but they don’t get nearly as much attention as what are seen as deficits. 

So here’s the other thing about the brain: It develops A LOT when you’re young. The amount of change you undergo as a child is huge. We’re born not able to control our own bodies, understand other people, or form abstract thought. Those are all things we develop as we mature. Kind of like how we go from the size of a football to five or six feet tall.

There’s an expected model for what “healthy development” looks like. Walking and talking occur around age one; the ability for concrete, abstract thought begins at age seven. 3-year-olds can be expected to understand the word “look”, 8-year-olds learn “examine”, 14-year-olds learn “perceive”. It’s the model tests are based on. The general assumption that 98% of children the same age will be in the same general area of brain development is why we group schools into classes by age.

But not everyone’s in that 98%. The 2% are neurodivergent.

I don’t think being neurodivergent means you’re innately worse or better than anyone else, any more than my 8 fingers means I’m not a human being. It’s just how we are. It’s not a choice we make, to have the brains or bodies we’re born with. The choice is what we do with them. But the problem is, being a 2%er in a 98% world, you’re assumed to be a 98%er who’s just choosing to be different. I have ADHD, meaning, difficulties in my brain to do with attention and control over my actions; but that wasn’t known when I was a child, so people just thought I was choosing to be inattentive and lazy. And I’m intellectually gifted, so when I finished a test in half the time it took everyone else, they thought I was choosing to show off. But I wasn’t; I try really hard to focus and pay attention, and I tried really hard to look “normal”. It was just like... constantly trying to slouch or stand on my tiptoes, to be a different height than I was. It didn’t work, and then I was also the weirdo who was contorting herself into funny positions.

Sometimes neurodivergent kids have needs that are poorly understood because of the lack of attention paid to them. For example, it’s known that Gifted kids are prone to emotional problems sometimes because their intellect develops faster than their ability to handle emotions--for example, a 4-year-old who loses the ability to form language when she’s hurt or scared, and who needs a comforting adult to help her deal with a skinned knee or a scary dream, could intellectually make the intellectual leap from “my dog died” to “I and everyone I love are going to die someday” and be totally unprepared to handle a thought that terrifying, and become inconsolable in a way that makes no sense to the adults around her--and she’s unable to explain, because she can’t use language when she’s upset yet. And even if she does, they might not expect a kid that little to have a thought that big, because most other 4-year-olds don’t.

It sounds like you didn’t put much more effort into developing your vocabulary than most other kids; you just happened to have a particularly good ability to absorb and remember new words. The words you’re using a very normal... for a small percentage of children your age. If they assigned classrooms based on vocabulary instead of age, you would be perfectly normal. It’s not like there’s some extra area stuck onto your brain that nobody else has; you’ve just developed differently. Would that neurodivergence show up on an IQ test if you took one now? I don’t know. I do know that IQ test results can vary a lot depending on when you take them, which test you get, and whether you’re having a good day. 

I also know that although IQ tests are designed, for the vast majority of people, to get the same general score on all the different areas, many neurodivergent people have a “differentiated profile” where their scores on the different subtests do not match the average. For example, you can score above average on tests to do with making things with your hand, but below average in using language. (Kids like this are often very frustrated in school, where they’re mistaken for being globally “slow” because they’re not able to make other people understand just how much is going on inside their heads.) Or you can be very good with spoken vocabulary, but very bad with spelling. The difference doesn’t have to be huge to make a difference, although sometimes people don’t think it matters. For example, my IQ scores were all the same, except for two subtests. In Coding and Digit Span, I scored two points below everything else. The psychologist who assessed me said, “Whatever, it’s still very high, no need to worry,” and wrote in his report that I was “very likely to enjoy academic success”.

Digit Span and Coding are two parts of that IQ test that best assess memory, attention, and focus. That difference meant something. If he’d looked closer, he might have seen that while I was a smart kid, I had ADHD. Buuut he didn’t, so I didn’t find out I had it until almost a decade later, when I was having a mental health crisis and had failed several university courses because I just couldn’t get my shit together (an ADHD trait).

The thing that identifying as Gifted gave me (because I read Stephanie Tolan’s Welcome to the Ark when I was 14) was the best understanding of where to find other weird kids like me. I started looking into weird and nerdy activities and groups (historical re-enactment, model parliament, science fiction conventions, advanced high school courses) that were likely to contain other weird and nerdy people. I thought: If it’s 2% of us who are different, then that’s 2 in a grade of 100 people. But it’s 20 in a school of 1000, 200 in a town of 10,000, 2000 in a city of 100,000. My people have got to be out there somewhere.

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Deadline Approaching for Biostatistics Assignment Help? Call Us Now!

What Is Biostatistics

Are you a geek in mathematics and want to stand out in the class by providing high-quality biostatistics assignments? Indeed, but do you know the best approaches and techniques for writing high-quality assignments? You are at the right place. Assignments help lite is an online assignments and homework writing help service provider. We excel in providing professional assistance and advice to the students for helping them get the best of the assignments.

Biostatistics is an application of statistical principles to the questions and problems in medicine, public health, and biology. The functions and principles are biostatistics are used in collecting and summarizing the data for analyzing and interpreting it.

This is an essential subject as it studies the important manners of dividing the questions and the problems and collecting data for the same, which is eventually used to solve the problems.

Issues Faced by Students While Writing Biostatistics Assignments

·         Lack of generating ideas: The students' ideas make the assignment and the homework more impressive for the university. When the students fall short of newer ideas, they fail to add creativity in the assignments, which eventually leads them to lose grades. The university is very particular when it comes to quality of writing and value-addition in the assignments. They expect the students to brainstorm various ideas, communicate with the professors and seniors and then curate the overall assignment or the homework. Biostatistics homework is considered to be a very tedious task for the students as they have to continuously study the dynamic forces and be creative. Biostatistics Homework Help is available for the students at assignments help lite as we have a team of subject-specific assignment writing experts who are concentrated on writing the best quality homework and assignments for the students.

·         Lack of resources: The resources are another essential part of the assignments and the homework written by the students. The students need to collect a lot of information and resources that include learning about how to make the assignment or homework valueable and  techniques that are supposed to be applied by the students to get better grades. The resources help students add quality to the assignment, which leads them to get better grades. Biostatistics Assignments are practical oriented assignments and concentrate on numbers; hence the students need to add quality yet make the assignments; solution-based and perform well to get good grades.

·     Insufficient guidance: The guidance plays a very important role in the quality addition of an assignment. The students must seek all kinds of professional and unprofessional guidance from the professors, the seniors and other authorities who could help them complete their assignments and homework with ease. Biostatistics Homework is assigned to the students to check their overall performance and learning during the tenure of graduation. Guidance from experts can help the students write effective and quality-oriented biostatistics assignments homework.

·         Format and structuring of the assignment: The assignments need to be properly structured and formatted to get the best grades and make the overall assignments impressive. The students are not aware of the techniques of writing the assignments with good quality; hence need biostatistics assignment help and biostatistics homework help.

Why Choose Assignments Help Lite for Your Biostatistics Homework Help and Assignment Help?

Assignments help lite has been helping students in completing their assignments for several years and has been able to develop a profound knowledge of writing assignments with absolute quality and value.

Assignments help lite is a team of professionals dedicated to writing the best of the assignments and homework for the students. Assignment writers are often misunderstood as standard assignment writers, but the scenario is different at assignments help lite as we have a set of professional subject experts who are graduates and PhD’s in different subjects and carry extensive knowledge of the subject. Their knowledge  helps them find better avenues for writing the assignments and making them look better.

Affordability:

One of the biggest issues students face when it comes to taking biostatistics homework and assignment help online is affordability. The students do not have an active income module and hence cannot manage to pay big amounts to complete their assignments. Assignments help lite has come up with the best services which are customized keeping in consideration the affordability range of the students. Why wait when you get all that you need in one place?

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Easy College Majors to Get a Degree

Are you considering earning a degree but are uncertain what major to pursue? Your area of study may be less important than you would expect. In fact, opting to earn an easy college degree may be the best solution, especially if you are not planning to enter a specific field. Careers in general administration or retail, for example, often require an advanced education but do not necessitate a specific focus. A degree of any kind will usually be sufficient.

It’s actually quite common for prospective students to choose a major that relates to a vocation they are not planning to pursue. This is because there are numerous benefits to earning a degree that are not career specific. An advanced education opens up a wide variety of opportunities that can lead to more overall happiness and stability later in life. Earning a degree of any kind often sets a strong foundation for greater personal and professional success.

Table of Contents

Overview

Degree Programs

Easy Majors

  Benefits of Earning Any College Degree

Regardless of major, there are numerous benefits associated with earning any college degree. Some of the most prominent reasons to pursue a degree include making more money, expanding your knowledge base, obtaining better career opportunities, and achieving job security.

Many people opt to earn a degree because they want to earn more money. While many fields offer entry-level employment to those without a higher education, most employers do offer graduates bigger salaries. This is particularly true for master and doctorate level degrees which most frequently lead to management and executive positions.

According to PayScale, bachelor’s degree graduates earn an average yearly salary of around $63,800, while master’s degree graduates make an average of $76,000 per year. This is significantly higher than the average $15 per hour that high school diploma recipients and certificate-holders make. In 2019, the Bureau of Labor Statistics (BLS) reported that full-time workers aged 25 and older who lacked degrees had median weekly earnings of $749, while workers with bachelor’s degrees had median weekly earnings of $1,281.

Degree graduates also enjoy better career opportunities. Colleges and universities design their curriculums, as well as all on-campus regulations and activities, to enhance student development. Regardless of major, anyone attending an institution is likely to attain and hone a wide range of skills that can be utilized in various fields. Employees who possess degrees are also commonly considered more valuable in the workplace, effectively increasing job security.

While many benefits relate to gaining employment after graduation, many others are more relevant in personal aspects of life. Other benefits include strong career outlook, decent financial compensation, and easily transferrable skills that create competitive candidates in the job market. In fact, there are possibly as many, if not more, personal reasons to attend college. Students often benefit from networking with peers, taking on leadership positions, experiencing alternative perspectives, developing new personal philosophies, and traveling through campus activities and study-abroad programs. Additionally, it is common to establish significant and lasting relationships with other students, staff, and faculty members while attending college.

What Makes a College Degree Easy?

Finding an easy college degree can be quite simple, although the results of any study on the matter would, by nature, be subjective. Something that seems easy to you may not be so simple for another person. This is why it is necessary to research options thoroughly before deciding to enroll in a program.

Consider using the following information to find the best solution for you:

Graduate GPA Data Find out which degrees produce graduates with the highest grade point averages (GPAs). This means that the majority of students enrolled in the program achieve high marks, which can indicate that the curriculum is fairly easy to complete. Identifying majors in this way can help you narrow down your list of prospects.

Student Reviews Students from colleges and universities all over the world can leave feedback about their experiences online. Read through reviews to find out if any degree programs are known for being particularly easy. It’s not uncommon for certain departments to gain a reputation for difficult or ease over time. You can also post in forums to inquire about which options may suit your needs best.

Course Requirements It may also prove helpful to examine curriculum listings and course descriptions prior to selecting a degree program. Most colleges and universities provide detailed information on their websites, making it easy to spot whether or not difficult classes may be required for graduation. Keep your personal skills and preferences in mind and avoid majors that necessitate taking courses you know you will struggle with, such as higher mathematics.

What to Consider When Choosing a Degree

There are several factors you should consider when looking for a degree program. Every college and university is unique. By comparing and contrasting important features, you can more easily determine which institution suits your needs best. Some of the most significant aspects include prospective career opportunities, salary projections, job outlooks, and possible work environments. You can also pull inspiration from your own natural talents, personal passions, and subjects of greatest interest. Again, you should consider avoiding subjects you are likely to have the most trouble with.

Ultimately, one of the most significant factors to consider is how much effort you are willing to put into pursuing an education. Earning an associate degree typically requires two years, whereas bachelor’s degrees generally take four years and master’s degrees take an additional two years to complete. Your options will vary depending on your dedication to achieving your academic and career goals.

Easiest College Degree Programs

While the process of determining which college degrees are easiest is fairly subjective, it is possible to identify which majors are generally the most difficult. Science, technology, engineering, and math (STEM) graduates have some of the lowest GPAs. Humanities and social science majors, on the other hand, trend towards the highest GPAs among academic disciplines.

Based on this, some of the easiest college programs include:

Business / Management Degrees in business and business management tend to be very broad in nature, touching on a wide variety of related topics. They tend focus on the development of skills that are useful in numerous industries and can be transferred from one position to another. This option is particularly relevant for undecided students interested in exploring several different subject areas. Additionally, business and business management are ideal for outgoing people who enjoy interacting with others. Note that some math classes may be required.

Communication / Media / Journalism Degrees in communication, media, and journalism focus primarily on writing, thinking, and formulating ideas cohesively. As humanities majors, they do not require any additional STEM classes, making them the perfect solution for creative-minded individuals. Read-and-respond assignments are common, as are personal presentations and projects related to current events.

Criminal Justice Degrees in criminal justice also tend to lack any significant focus on STEM subjects. Instead, these majors introduce students to the history and current functionality of the nation’s legal system. There are numerous career opportunities within the field and many of the skills attained are easily transferrable to other jobs. Students rarely have to depend on memorization and they can gain significant experience from internships and on-the-job training.

Education Degrees in education focus on pedagogy (teaching methods), which means students only need to take STEM classes if they choose to teach one of those subjects. Excluding prospective science and math teachers, very little technical knowledge is needed to be successful in this field. Depending on the age group being taught, it’s possible the majority of knowledge needed will relate to subjects already learned previously.

History Degrees in history also lack the need for extensive STEM coursework. These majors tend to place more focus on learning about past events, both in the United States and around the rest of the world. Like communication and journalism, this field is more likely to require extensive reading and writing assignments with a focus on contextualizing the information. Additionally, students studying history may need good memorization and critical thinking skills.

Psychology Degrees in psychology may not be as easy as some of the others listed here. This is largely due to the fact that students will likely need to complete some higher-level math courses. Additionally, a significant amount of material must be memorized in order to pass examinations, graduate, and the fact that you will need a master’s degree to become licensed to practice. The skills learned in this major can be easily applied to almost any industry, however, making this option extremely viable for students who have not identified specific career goals yet, even if they only plan to earn a bachelor’s.

Social Sciences / Sociology Degrees in social sciences and sociology are similar, requiring some math classes that may be considered too boring or hard for some students. Like psychology majors, these programs tend to be a middle-of-the-road option in terms of difficulty. Individuals who enjoy critical thinking, however, as well as comparing and contrasting information, are likely to do well in this field.

Easy Majors for Students with Specific Talents

It’s also important to realize that some majors will seem easy for certain people if they possess a particular talent or long-standing interest in them. Choosing a degree base on these factors is, of course, completely subjective. Consider your skills and passions carefully before deciding which program suits your academic and career aspirations best. You can start this process by thinking about which subject areas you were most proficient in during high school and making a list of all your extracurricular activities. It may also prove beneficial to speak with some of your past teachers and/or the school guidance counselor for assistance in pinpointing which areas suit you best.

Accounting / Mathematics The subjects of accounting and mathematics simply make sense to some people. Individuals who are mathematically inclined probably did well in advanced geometry, trigonometry, and calculus classes during high school. They often enjoy working with numbers and are capable of identifying patterns in data.

Arts (Fine Arts) Talent in fine arts can come naturally or result from significant practice. Even natural talent must be honed, which means individuals interested in this subject tend to spend a lot of time working on creative projects. They are likely to excel in arts-related classes during high school and may gravitate towards fine arts clubs as well.

Biology Biology is typically a good fit for people who have a strong interest in or intense passion for living organisms. These individuals likely do well in most science classes, but are particularly fond of lab and dissection assignments. Biology majors are unique because they can lead to a number of great employment opportunities, from studying animals and engineering plants to decoding genomes and providing medical care. However, you should be aware before choosing this major that it often includes a inordinate amount of memorization.

Computer Science Computer science is not for everyone, but those who do major in this subject have some of the best career prospects available. Those with a love for mathematics, analytical thinking, and problem solving will thrive most in this field. These individuals tend to enjoy learning in general, but are particularly inclined to utilize various forms of technology.

English Students who did will in English and history classes during high school make good English majors in college. Programs tend to require a lot of reading and writing assignments, which means those who enroll should have a passion for both areas. People who regularly participate in programs like Battle of the Books or spend time writing creatively are likely good candidates.

Exercise Science Exercise science programs explore how the body and mind function during exercise. People who are athletically inclined tend to do well in this field because they have a good understanding of and enjoying being physically active. Students who do well in exercise science likely participate in and enjoy various sporting activities. It’s important to note, however, that earning a degree in exercise science will place the primary focus on theory, not activity.

Foreign Language Majoring in a foreign language is more than just learning to speak another language; it also consists of learning about the culture of the place where it is most commonly spoken. This means that students who choose to pursue a language degree often have a strong interest in and passion for a specific region in the world. They often grew up speaking two or more languages at home or greatly enjoyed their foreign language courses in high school and loved the idea of being able to communicate more fully in their chosen foreign language.

Graphic Design Graphic design is most appealing to people who are visually oriented, creative, and interested in technology. In high school, these students likely excelled in both art and computer classes. They likely have familiarity with various graphics-related fundamentals including typography, color theory, and 3D imagery.

Marketing Marketing majors learn how to develop and brand products or services for the companies or organizations they will work for. As high school students, those who will do best in this field likely showed interested in finance and communication. They may have done will in math classes and/or joined business clubs.

Music Those who are naturally talented at musical composition and/or playing a musical instrument will find majoring in music most appealing. In high school, they likely participated in band class, sang in the choir, or played an instrument at sporting events. It’s also probable that these students attended band camps or received private lessons from musical professionals.

Visual and Performing Arts Visual and performing arts will be most appealing for creative and emotionally aware individuals who enjoy acting. They likely participated in drama classes and clubs during high school. These students also tend to have a strong passion for dramatic writings and enjoy performing in front of other people.

Easy College Majors to Get a Degree Find more on: universityhq.org/

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Deadline Approaching for Biostatistics Assignment Help? Call Us Now!

What Is Biostatistics

Are you a geek in mathematics and want to stand out in the class by providing high-quality biostatistics assignments? Indeed, but do you know the best approaches and techniques for writing high-quality assignments? You are at the right place. Assignments help lite is an online assignments and homework writing help service provider. We excel in providing professional assistance and advice to the students for helping them get the best of the assignments.

Biostatistics is an application of statistical principles to the questions and problems in medicine, public health, and biology. The functions and principles are biostatistics are used in collecting and summarizing the data for analyzing and interpreting it.

This is an essential subject as it studies the important manners of dividing the questions and the problems and collecting data for the same, which is eventually used to solve the problems.

Issues Faced by Students While Writing Biostatistics Assignments

Lack of generating ideas: The students' ideas make the assignment and the homework more impressive for the university. When the students fall short of newer ideas, they fail to add creativity in the assignments, which eventually leads them to lose grades. The university is very particular when it comes to quality of writing and value-addition in the assignments. They expect the students to brainstorm various ideas, communicate with the professors and seniors and then curate the overall assignment or the homework. Biostatistics homework is considered to be a very tedious task for the students as they have to continuously study the dynamic forces and be creative. Biostatistics Homework Help is available for the students at assignments help lite as we have a team of subject-specific assignment writing experts who are concentrated on writing the best quality homework and assignments for the students.

Lack of resources: The resources are another essential part of the assignments and the homework written by the students. The students need to collect a lot of information and resources that include learning about how to make the assignment or homework valueable and  techniques that are supposed to be applied by the students to get better grades. The resources help students add quality to the assignment, which leads them to get better grades. Biostatistics Assignments are practical oriented assignments and concentrate on numbers; hence the students need to add quality yet make the assignments; solution-based and perform well to get good grades

Insufficient guidance: The guidance plays a very important role in the quality addition of an assignment. The students must seek all kinds of professional and unprofessional guidance from the professors, the seniors and other authorities who could help them complete their assignments and homework with ease. Biostatistics Homework is assigned to the students to check their overall performance and learning during the tenure of graduation. Guidance from experts can help the students write effective and quality-oriented biostatistics assignments homework.

 Format and structuring of the assignment: The assignments need to be properly structured and formatted to get the best grades and make the overall assignments impressive. The students are not aware of the techniques of writing the assignments with good quality; hence need biostatistics assignment help and biostatistics homework help.

Why Choose Assignments Help Lite for Your Biostatistics Homework Help and Assignment Help?

Assignments help lite has been helping students in completing their assignments for several years and has been able to develop a profound knowledge of writing assignments with absolute quality and value.

Assignments help lite is a team of professionals dedicated to writing the best of the assignments and homework for the students. Assignment writers are often misunderstood as standard assignment writers, but the scenario is different at assignments help lite as we have a set of professional subject experts who are graduates and PhD’s in different subjects and carry extensive knowledge of the subject. Their knowledge  helps them find better avenues for writing the assignments and making them look better.

Affordability:

One of the biggest issues students face when it comes to taking biostatistics homework and assignment help online is affordability. The students do not have an active income module and hence cannot manage to pay big amounts to complete their assignments. Assignments help lite has come up with the best services which are customized keeping in consideration the affordability range of the students. Why wait when you get all that you need in one place?

Call or contact assignments help lite now!

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Covariance & Contravariance

Through this article, we are going to take a look at some terms like "covariance" and "contravariance" to understand to which concepts they are related to.

Introduction

Sometimes in the happy and sparkling world of programming, we can meet some terms that we have hardly heard before. More often, those terms are borrowed from other domains and seem to hide very advanced concepts while, indeed, they encapsulate very simple ideas.

A small definition

Covariance and contravariance come from mathematics. It is a measure of how changes in one variable are associated with changes in a second variable. It measures the degree to which two variables are linearly associated. In other words, it describes what happens when a change occurs. If the result goes in the same direction as the change, it is covariant, otherwise it is contravariant.

We are not going to dig deeper with mathematical notions. We are rather going to take a look at how these concepts are translated in the world of computer science. First, we have to understand Subtyping.

Subtyping

Subtyping is a notion where a subtype, which is a data type, is related to a supertype. Subtypes are an essential concept in object-oriented programming and are substitutable to supertypes. There is a difference between Inheritance and Subtyping and it can be defined like so:

Subtyping refers to compatibility of interfaces. A type B is a subtype of A if every function that can be invoked on an object of type A can also be invoked on an object of type B.

Inheritance refers to reuse of implementations. A type B inherits from another type A if some functions for B are written in terms of functions of A.

In other words, Subtyping refers to the compatibility of interfaces. Inheritance refers to reuse of implementations. Subtyping is about implementing an interface, and so being able to substitute different implementations of that interface at runtime. Inheritance is about gaining attributes and functionalities of super types.

Subtyping relation is defined by the type system of a programming language. A type system is a set of rules that assigns a type, which is a property, to the various constructs of a program (variables, expressions, functions, modules). The way to assign types is defined by type rules. A programming language has primitive data types. Those basic types are considered to be built using nullary type constructors, or, in other words, constructors without any argument. A type constructor is a feature that builds new types from old ones. A type constructor is an n-ary (number of arguments) type operator taking as argument zero or more types, and returning another type.

Object hierarchies and substitution

Covariance and contravariance have a slightly different meaning in programming than in mathematics. The idea is related to the hierarchy of types.

Let's say we have two classes, A and B. Let's say that B is derived from type A. So, in other words, A is the base class for B. So B contains every method and property that type A does and more. So, we can say that B is "bigger" than A. So, here we have a way of ordering classes. We can also say that A is higher in the type hierarchy than B.

If B derives from A, it means that it contains everything that A contains. So, we can use B anywhere that we could have used A. Of course, we can't always use A in place of B. The relationship is asymmetrical. This is formally known as the Liskov Substitution principle. This principle also states that everything that is true for A should be true for B.

Formal definitions

Knowing what we know, let's try to elaborate some formal definitions.

A typing rule or a type constructor is:

covariant if it preserves the ordering of types, which orders types from more specific to more generic

contravariant if it reverses this ordering

bivariant if it is covariant and contravariant at the same time

invariant or nonvariant if it is neither covariant or contravariant

So, we can say that Covariance and contravariance are about very specific situations, where we can treat one type as if it were another type in a certain context. Covariance allows a "bigger", or less specific, type to be substituted in an API where the original type is only used in an "output" position. contravariance allows a "smaller", or more specific, type to be substituted in an API where the original type is only used in an "input" position. Covariance and contravariance are the ability of a programming language to take advantage of commonalities between generic types deduced from known commonalities of their type arguments.

Examples

Let's try to use examples to illustrate a little more what we have seen until now. Let's imagine that we have the following class:

public class Person { public string Name { get; set; } }

Now, we have a derived class:

public class Client : Person { }

Let's now imagine the following classes:

public class MailingList { public void Add(IEnumerable<out Person> persons) { } } public class Company { public IEnumerable<Client> GetClients() { } }

We can now make the following operations:

var clients = company.GetClients(); var mailingList = new MailingList(); mailingList.Add(clients);

Here, we use a more derived type, Client, with the Add() method. So, this last method is covariant. Covariance allows us to pass a derived type where a base type is expected.

Let's now try to illustrate contravariance. Let's imagine the following base class and derived class:

class A { } class B : A { }

Suppose that we have a delegate:

public delegate A MyDelegate(B b);

Now can imagine the following code:

class Program { static A Method1(A a) { Console.WriteLine("Method 1"); return new A(); } static B Method2(B b) { Console.WriteLine("Method 2"); return new B(); } static void Main(string[] args) { MyDelegate myDelegate = Method1; myDelegate(new B()); }

}

contravariance allows a method with the parameter of a base class to be assigned to a delegate that expects the parameter of a derived class.

Conclusion

Through this article we took a look at the concepts of Covariance and contravariance. We saw that those terms were borrowed from mathematics and are relative to Subtyping, more specifically to object hierarchies and substitution. We saw that Covariance allows us to pass a derived type where a base type is expected. On the other hand, contravariance allows a method with the parameter of a base class to be assigned to a delegate that expects the parameter of a derived class.

One last word

If you like this article, you can consider supporting and helping me on Patreon! It would be awesome! Otherwise, you can find my other posts on Medium and Tumblr. You will also know more about myself on my personal website. Until next time, happy headache!

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The primary function of the job is performing a wide variety of turbine layout/fitting, assembly, blading, welding required to complete fully assembled turbine components.

If selected for this position you will be assigned to work a 4×10 Night shift schedule, Monday – Thursday.

What are your job responsibilities and requirements?

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What are your minimum requirements for your role?

Minimum education required is a high school diploma or GED equivalent

Minimum of 2-5 yrs of Industrial Welding Experience

Be able to successfully pass or provide credentials for successful completion of CRC to include Industrial Reading, Math, Blueprint and Metrology written test.

Ability to pass a 6G Inconel Test weld test.

Ability to pass standard hearing, vision, and PFT tests.

Ability to use basic shop math; precision measuring equipment.

Ability to obtain fork truck and crane license.

Applicants must be legally authorized for employment in the United States without need for current or future employer-sponsored work authorization.

Siemens Energy is a global pacesetter in energy, helping customers to meet the evolving demands of today’s industries and societies. SE comprises broad competencies across the entire energy value chain and offers a uniquely comprehensive portfolio for utilities, independent power producers, transmission system operators and the oil and gas industry. Products, solutions and services address the extraction, processing and the transport of oil and gas as well as power generation in central and distributed thermal power plants and power transmission in grids. With global headquarters in Houston in the U.S. and more than 64,000 employees in over 80 countries, Siemens Energy has a presence across the globe and is a leading innovator for the energy systems of today and tomorrow, as it has been for more than 150 years.

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Organization: Siemens Energy

Company: Siemens Energy, Inc.

Experience Level: Early Professional

Job Type: Full-time

Equal Employment Opportunity Statement Siemens is an Equal Opportunity and Affirmative Action Employer encouraging diversity in the workplace. All qualified applicants will receive consideration for employment without regard to their race, color, creed, religion, national origin, citizenship status, ancestry, sex, age, physical or mental disability unrelated to ability, marital status, family responsibilities, pregnancy, genetic information, sexual orientation, gender expression, gender identity, transgender, sex stereotyping, order of protection status, protected veteran or military status, or an unfavorable discharge from military service, and other categories protected by federal, state or local law.

EEO is the Law Applicants and employees are protected under Federal law from discrimination. To learn more, Click here.

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