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Mathematics is a rules based system. The rules guarantee that you can reach true conclusions from assumptions that you may assume are true. You understand mathematics when you know the rules and know how to use the rules to build more complex derivations, in order to establish properties that follow the given assumptions.
A new way of writing math
Structured derivations
Structured deviations (SD) is a language for constructing mathematically correct deviations. Writing your solution as a structured derivation will improve your understanding of mathematics and teaches you how to reason in a mathematically correct way. A structured derivation shows explicitly the logical structure of the argument, and makes it easy to correct any errors found.
SD editor
The SD editor makes it easy to build and edit a structured derivations. You can build your solution step by step, adding, deleting and modifying steps as needed, as the solution idea becomes clearer during the solution process.
SD checker
The SD checker goes through a structured derivation step by step, and marks each step as either proved correct or unproved. A step that is unproved is usually wrong, but it is possible that the proof was just too difficult for the checker to find. Fix the error steps and check again. Iterating will eventually lead you to a correct solution of the original problem.
The videos below show how to solve mathematical problems with structured derivations, the digital editor, and the automatic checker. For a more detailed explanation, check out the “How to get started” tutorial in eMathStudio. (Videos in preparation)
Getting started
Algebraic calculations
Solving equations
Solving a word problem
A new way of learning math
Mastery learning
Mastery learning is a method for individual learning that is known to give very good learning results. A subject is divided into a number of successive topics. Each topic consists of a theory part and a collection of assignments. You need to solve at least 80% of the required assignments for a topic to be considered as having mastered the topic. Only then can you continue with the next topic. This guarantees that you leave no gaps in your understanding of the subject.
The eMath learning method
The eMath method for learning mathematics uses structured derivations together with the SD editor and the SD checker to solve mathematical problems, in combination with mastery learning. The SD checker gives you immediate and personal feedback on your own solutions, which makes it easier to find correct solutions to the topic assignments.
eMathStudio
eMathStudio is a digital learning environment for mathematics that supports the eMath method. It can be used for solving mathematical problems on your own, or for self-studies on some math subject, or for taking online math courses. There is a free version of eMathStudio that you can use without registration. However, more demanding use require a paid subscription.
The videos below show how to study in eMathStudio, and how to use eMathStudio as a note taking app, where you can work out issues that come up in the course and share your notes with others.(Videos in preparation)
The eMathStudio learning environment
The first video below gives an overview of eMathStudio learning environment, what you can do in the different rooms there. Find out more about the environment in the “Overview of eMathStudio” tutorial. The second video describes in more detail how to study ahn eMat course for yourself, and how this differs from participating in tutored eMath course. (Videos in preparation)
Subscription plans
Free use
eMathStudio is an excellent environment for taking notes with mathematical content. You can use it freely, without registration or subscription, for writing notes, using the SD editor, saving notes on your own computer, print them as pdf or export them to Latex format. You also have limited use of the SD checker to check your notes. You will, however, need a basic subscription for more substantial checking.
Note taking
The basic subscription package provides free use of the SD editor and a large quota for SD checks. You can share your notes with others, and collect your notes into Notebooks for different subjects. This package is useful for anybody who wants to have a flexible environment for writing down and checking notes with a mathematical content.
Self-studies
The self-study subscription comes with a textbook that you study topic for topic. The system keeps track of your progress using mastery learning. You solve the assignments with the SD editor. The SD checker, which gives you immediate and personal feedback on your own solutions. The self-study books are great for learning a mathematical subject area, or for rehearsing some area for exams etc.
Online courses
The course subscription allows you to participate in an online math courses. It is essentially a self-study course but with a human tutor that gives you feedback on your solutions when you have problems, helping you when you get stuck. You can start an online course anytime during a given period (usually 4 months), but need to finish it before the period ends. You study at your own individual pace.
Try out eMathStudio
Try out eMathStudio (without registration and subscription) to see how it suits your needs. You can subscribe later to the features of the environment that you find useful.