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I guess below college there are only 学科, and in college or even higher (if any) both 学科 and 专业 are merged as the same. That's why this year's first-rate university and 学科 evaluation does not include 专业.

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When we talk about the courses we choose in college, they are pretty much the same thing, but actually they are just different from the purposes of their courses.

学科 is for academic purpose, studying a certain science or academic field.

专业 is based on social professions and the social division of labor, learning skills and knowledge of a certain industry or business.

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In this context, 学科 means 'subject/ course' For example, 'mathematics'(数学科) and 'art' (艺术科) are both subject/ course you can pick in university. One can be 'major in mathematics' and 'minor in Art'

专业 is short for '学科专业'(subject major)' as in 'major in physics' (物理专业/主修物理)

From Google Translate

学科专业- major

  • I understand a college student has to learn a number of 学科 in his or her 专业. – NanningYouth Oct 4 '17 at 7:36
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There also seems to be a diffence in usage betweeen Taiwan and mainland China: In the latter, 专业 generally refers to your major or field of study, while in the former 主修 (more literally "major") is used instead.

To answer your question (as a non-native), you could say something like 虽然我的专业是数学,但我还是觉得别的学科都是有价值的。("Even though my major is maths I still think that other academic disciplines have a certain worth.")

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學科 has two general meaning:

  1. Subjets that are distinguish due to the content of the knowledge.
  2. A collectively calling of all the paper knowledge, to apart from 術科 (subject or course in military/physical/design training, any training that is not associated with studying books)

專業 we normally take it's meaning as "Profession"

When talking about "專業" in college courses, we normally refer to the category of "專業科目" (professional courses), which normally happens to be the courses related to students major, or even more difficult.

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