Final answer:
Correct statements about Muslim achievements in science and mathematics include the introduction of algebra and the influential medical work of Ibn Sina. The claim that Muslim scholars did not surpass European accomplishments in their time is a misconception.
Step-by-step explanation:
The statements that correctly describe Muslim achievements in science and mathematics are:
A. Muslim mathematicians introduced algebra into the world. Contributions from scholars like Muhammad ibn Musa al-Khwarizmi led to the development of algebra, which has had a profound impact on mathematics. B. Ibn Sina collected medical knowledge into a book that was used for centuries in Europe. Ibn Sina, also known as Avicenna, is recognized for his significant contributions to medicine and his works were highly influential. D. Muslim scholars made some advances in science and mathematics, however, the statement that they could not surpass European scholars in the same time period is a misconception, as the Muslim scholars' contributions to science and mathematics were foundational to the Renaissance and beyond.
Statement C is incorrect as Muslim medicine was known and respected beyond the Arabian Peninsula, notably influencing Europe.