Abstract: Architecture for a word processing application that facilitates operating on mathematical symbols, expressions, and/or equations input to a word processing document, and returning results back to the document. User input to the document in the form of math symbols, expressions or equations is transformed into a format for processing by a math engine. The engine returns one or more operations to the user that can be performed on the input, including calculating mathematical solutions, graphing equations and viewing steps to solving math problems. A user interface allows the user choose from the possible operations and to interactively manipulate input and graphs in the word application. The results can be inserted directly into the document and also be graded automatically.

Abstract: Systems and methods for use in handwriting recognition in computer algebra are provided. One disclosed method includes receiving handwriting input from a user via a handwriting input device, the handwriting input representing a mathematical expression. The method further includes, at a recognizer, processing the handwriting input to recognize a plurality of candidates and ranking the plurality of candidates to form initial candidate data. The method may further include, at an application program, scanning the plurality of candidates for segments that match application-level criteria, and adjusting a rank of one or more of the plurality of candidates based on the matching, to form a processed candidate list. The method may further include displaying the processed candidate list via a graphical user interface.

Abstract: Systems and methods for identifying asymptotes in approximated geometric forms are provided. One disclosed method includes identifying a set of data points that represent an approximated geometric form. The data points may be organized into segments. The method may further include determining a visible range of the geometric form to display. The method may further include looping through successive segments of the approximated geometric form, and on each loop, for a current segment, making a decision whether to draw the current segment based upon a prediction of whether the current segment traverses an asymptote within the visible range. The method may further include displaying on a graphical user interface of a computing device, a graph of the segments of the geometric form in the visible range, the graph not including those segments that were decided not be drawn.

Abstract: A problem checker architecture that monitors user progress during a problem-solving process and assists the user through the process (e.g., when requested) using common human methods of solving the problem. Assistance can be in the form of detecting errors during the process, and providing context-sensitive help information when the user gets stuck or makes a mistake. The problem checker can walk the user through the process of solving a math problem one step at a time allowing the user to learn to solve math problems according to a number of different methods. Rather than simply calculating and displaying the answer, the problem checker allows the user to attempt to solve math problems, providing direction only when asked and correction only when required. The problem checker can recognize multiple solution methods for many common math problems and guide the user to the solution via any of the methods.

Abstract: A method and system for optimizing memorization of stored content. One or more discrete units of content selected for memorization are obtained. The units of content as displayed to the user according to a pre-determined order. Feedback is received from the user indicating the level of memorization achieved by the user corresponding to the displayed units of content. The subsequent order to display content is adjusted to achieve an optimized order for memorization based on the feedback received.

Abstract: A centralized view and management of stored variables for calculators and pieces of software emulating calculators is provided. Users can glance at the status bar and know what variables are stored. A single click then brings up a window within which a list of the stored variables and their values is shown. In this window users can clear individual variables or the entire variable list. Users can be reminded that their calculations contain stored variables by displaying the stored variable names in one or more different colors so that errors can be easily detected and corrected.

Abstract: Systems and methods for use in handwriting recognition in computer algebra are provided. One disclosed method includes receiving handwriting input from a user via a handwriting input device, the handwriting input representing a mathematical expression. The method further includes, at a recognizer, processing the handwriting input to recognize a plurality of candidates and ranking the plurality of candidates to form initial candidate data. The method may further include, at an application program, scanning the plurality of candidates for segments that match application-level criteria, and adjusting a rank of one or more of the plurality of candidates based on the matching, to form a processed candidate list. The method may further include displaying the processed candidate list via a graphical user interface.

Abstract: Systems and methods for identifying asymptotes in approximated geometric forms are provided. One disclosed method includes identifying a set of data points that represent an approximated geometric form. The data points may be organized into segments. The method may further include determining a visible range of the geometric form to display. The method may further include looping through successive segments of the approximated geometric form, and on each loop, for a current segment, making a decision whether to draw the current segment based upon a prediction of whether the current segment traverses an asymptote within the visible range. The method may further include displaying on a graphical user interface of a computing device, a graph of the segments of the geometric form in the visible range, the graph not including those segments that were decided not be drawn.

Abstract: Systems and methods for progressively parsing user input of a mathematical expression are provided. One disclosed method includes looping through characters in an input string, and on each loop, extracting a next token from the input string and determining a current grammar context based on the token or tokens extracted thus far. If it is determined that the current grammar context matches a predetermined condition, then the method may include modifying the tokens extracted from the input string in a predetermined manner associated with the predetermined condition. A parsing result may be obtained based on the modified tokens. The parsing result may be converted to a modified input string.

Abstract: A problem checker architecture that monitors user progress during a problem-solving process and assists the user through the process (e.g., when requested) using common human methods of solving the problem. Assistance can be in the form of detecting errors during the process, and providing context-sensitive help information when the user gets stuck or makes a mistake. The problem checker can walk the user through the process of solving a math problem one step at a time allowing the user to learn to solve math problems according to a number of different methods. Rather than simply calculating and displaying the answer, the problem checker allows the user to attempt to solve math problems, providing direction only when asked and correction only when required. The problem checker can recognize multiple solution methods for many common math problems and guide the user to the solution via any of the methods.

Abstract: Architecture for a word processing application that facilitates operating on mathematical symbols, expressions, and/or equations input to a word processing document, and returning results back to the document. User input to the document in the form of math symbols, expressions or equations is transformed into a format for processing by a math engine. The engine returns one or more operations to the user that can be performed on the input, including calculating mathematical solutions, graphing equations and viewing steps to solving math problems. A user interface allows the user choose from the possible operations and to interactively manipulate input and graphs in the word application. The results can be inserted directly into the document and also be graded automatically.

Abstract: A problem generator that takes an input as a math problem, analyzes the math problem, and intelligently spawns similar example problem types. The output is a set of math problems based on the conditions set during analysis and customization. For example, if the original problem deals with linear equations, this will be detected during analysis and used to spawn other linear equations as problems. Moreover, if the answer to the original problem is in integer format, so will the answers to the spawned problems. A customizable UI is designed to allow further customization of problem conditions to generate an accurate set of problems based on the initial input. Problem generator templates can be created, shared and modified for distribution and/or future use. Additionally, problem generation APIs can be extended for external code to automate and consume generated math problems.

Abstract: A centralized view and management of stored variables for calculators and pieces of software emulating calculators is provided. Users can glance at the status bar and know what variables are stored. A single click then brings up a window within which a list of the stored variables and their values is shown. In this window users can clear individual variables or the entire variable list. Users can be reminded that their calculations contain stored variables by displaying the stored variable names in one or more different colors so that errors can be easily detected and corrected.