The Rama 246:4 rules explicitly that it is absolutely prohibited according to Halachah to engage in a curriculum of secular studies. To read secular studies now and then, is permitted, he says. The source of the Rama is the Yerushalmi Sanhedrin.
It has been suggested the difference between a curriculum and just a glance, is that this prohibition is not due to Bitul Torah but rather a Bizayon HaTorah, by establishing studies in areas other than Torah, it shows that you believe they have some value that would justify learning them when you could have been learning Torah.
Rav Shimon Schwab ZT’L sought the Torah opinions of two great authorities, Rav Boruch Ber Liebowitz ZT’L and Rav Elchonon Wasserman ZT’L, regarding college education. Their responses were as follows:
Conclusion of Birkas Shmuel (Kiddushin #27 p.42): Universities and gymnasiums (i.e. secondary schools) are prohibited because of Apikursus [that they teach]… To learn secular studies on a regular basis is prohibited, as per the Rama 246:4 …
Kovetz Shiurim II:47: If you must learn books that contain apikursus, it is prohibited … needless to say even to make money or to prevent a loss thereof… If you learn secular studies in order to know a skill to make a living, it is permitted, and it is a Mitzvah. However, this is only in general. But if a person sees that his son wants to learn Torah and he is prepared to be a Gadol B’Torah, in such a case R. Nehuray said: “I will forgo all skills in the world and teach my son only Torah.”…
Rav Moshe Feinstein ZT’L also denounced college in a Teshuva, and in a famous speech delivered to his students, published under the title “The Counsel of the Wicked” (Vaad LeHaromas Keren HaTorah, New York, 1978). There is a tape available in many Seforim stores called “The prohibition to learn in Colleges” (Yiddish), which contains addresses by Rav Moshe Feinstein ZT’L and Rav Aharon Kotler ZT’L condemning college.
Regarding High School, the only reasons it is allowed is either because education is mandated by State Law (in New York it is until age 17), or simply because if they did not have High School education in the Yeshivas, parents would simply send their kids to worse places to get it.
HaRav Aharon Leib Shteinman said ( six years ago) to shun secular education. He concluded his remarks, commenting: “What is education today? Education is Torah! And more Torah! Whoever seeks happiness should teach his son Torah.”