Abstract: Methods, systems, and devices are described that enable the parsing and interpretation of common types of math problems in multiple choice format that are found in math textbooks and standardized tests.

Abstract: A strain and crack sensor senses an amount of strain induced in an object. A receiving planar antenna has a first resonant frequency and is configured to receive a querying signal at the first resonant frequency. A transmitting planar antenna has a second resonant frequency that is twice the first resonant frequency. At least one of the receiving planar antenna and the transmitting planar antenna is bonded to the object so that at least one of strain induced in the object or a crack formed in the object causes a shift in at least one of the first resonant frequency or the second resonant frequency. A matching element is in electrical communication with the first planar antenna and the second planar antenna. The matching element is configured to cause the transmitting planar antenna to radiate a response signal in response to the querying signal.

Abstract: A strain and crack sensor senses an amount of strain induced in an object. A receiving planar antenna has a first resonant frequency and is configured to receive a querying signal at the first resonant frequency. A transmitting planar antenna has a second resonant frequency that is twice the first resonant frequency. At least one of the receiving planar antenna and the transmitting planar antenna is bonded to the object so that at least one of strain induced in the object or a crack formed in the object causes a shift in at least one of the first resonant frequency or the second resonant frequency. A matching element is in electrical communication with the first planar antenna and the second planar antenna. The matching element is configured to cause the transmitting planar antenna to radiate a response signal in response to the querying signal.

Abstract: Methods, systems, and devices are described that provide for entry of hybrid mathematical and natural language statements in a mathematical notation friendly language and system for a rigorous yet practically tractable formal grammar to distill the essence of natural math notation. Hybrid statements mixing natural language and symbolic expressions including assertions, commands, queries, and/or deductions may be entered that are processed according to natural language processing. The statements, along with the math objects are evaluated, and one or more results output. Furthermore, systems may provide automatic construction of one or more solution narratives that can be beneficial to student users pedagogically.

Abstract: Methods, systems, and devices are described that provide for entry of hybrid mathematical and natural language statements in a mathematical notation friendly language and system for a rigorous yet practically tractable formal grammar to distill the essence of natural math notation. Hybrid statements mixing natural language and symbolic expressions including assertions, commands, queries, and/or deductions may be entered that are processed according to natural language processing. The statements, along with the math objects are evaluated, and one or more results output. Furthermore, systems may provide automatic construction of one or more solution narratives that can be beneficial to student users pedagogically.