What's the meaning of "receive credit for freshman mathematics" in college?

Question

This context comes from the book "Black Rednecks And White Liberals" by Thomas Sowell.

At one time, the reputation of Dunbar graduates was such that they did not have to take entrance examinations to be admitted to Dartmouth, Harvard, and some other selective colleges.22 When Robert N. Mattingly graduated from the M Street School in 1902, he entered Amherst College, receiving credit for freshman mathematics and first-year college physics— and he graduated in three years, Phi Beta Kappa. Yet, far from being one of the elite, Mattingly was, in his own words,“at Amherst on a shoestring.”

1. does "credit" in this context mean Official certification or recognition that a student has successfully completed a course of study(American Heritage® Dictionary)?

2. This sentence is confusing because "freshman" & "first year" mean the same thing therefore I don't know whether the author meant the first year of college or the school that this person was attending before they graduated and went to college. How to tell the difference?

If Robert N. Mattingly entered college receiving credit for freshman mathematics and first-year college physics does it mean he didn't have to pursue studies that included this scope of the curriculum and was able to start out his college studies further in terms of the curriculum of that university?

Answer 1

Dunbar is a high school located on M Street in Washington D.C..

The school's reputation was so great that when Dunbar graduate Mattingly entered Amherst College, Amherst automatically gave him two first-year college credits just because he went to Dunbar. This advantage helped him graduate in three years, rather than the usual four years.

The intended difference between "freshman" and "first-year" is unclear.

Answer 2

1. In all likelihood, every student entering Amherst as a freshman in 1903 either had to take a course called Freshman Mathematics (corresponding to Math 101 or something similar in colleges today) or had to place out of it—either by demonstrating mastery of the subject matter on a test or by having graduated from a high school of sufficient reputation that such mastery was assumed by Amherst administrators. The system for attaining a degree entails accumulating credits for the various required and elective courses one takes during one's time at college or university; completing a year-long course in freshman mathematics might yield four credits toward the total number needed for a degree. Evidently, in placing out of Freshman Mathematics, one automatically received those four (or however many) credits without taking the course.

2. Whereas "freshman mathematics" seems to have been a required course for all Amherst freshmen in 1903, it may be that not all students were required to take a class in physics, depending on what sort of degree they were working toward. But whether the course was required at some point in a student's college career or not, students weren't required to take it during freshman year. The idea behind the term "first-year college physics" is not "physics for first-year college students" but "first-year physics out of multiple years of physics classes offered." A student presumably could take first-year physics as a freshman but was not required to do so; moreover, a student could take the class as a sophomore, junior, or senior as long as doing so didn't cause problems with completing all of the (other) requirements for the degree that the student was pursuing.