what is the philsophy of home economics education?

Wouldn't this vary with time, culture, and many other factors? And from school to school?

I remember in the 1950's at the University...most subjects were taboo for women to take, such as engineering, business, math. For women, it was Education, or Home Economics, and frankly, the Home Ec route was a path to the Mrs degree.
Times have changed. Women can take any subjects, and do. Home Ec has changed greatly.
If I had to point a "philosophy" for Home Ec, I think I would work at the idea that the science and art of managing ones personal family life can be broken into teachable units, and mastered.

To follow up on this, most schools have changed the name of the Department of Home Economics to the Department of Family and Consumer Science. The department head at my univeristy complained for many years that the public thought of them as the "cooking, sewing, and cleaning" department. And of course they did much more than that. Changing the name of the degree was/is a step in changing the public's perception of what a "home ed" major does.

what are the ways to retain vitamins when preparin, processing and cooking food?

By cooking with steam intead of frying baking may also woork on the oven

There are several ways to retain vitamins when preparing, processing, and cooking food. Here are some tips:

1. Choose fresh produce: Fresh fruits and vegetables typically have higher vitamin content compared to frozen or canned varieties. Opt for fresh produce whenever possible.

2. Minimize exposure to heat: Vitamins are sensitive to heat and can be easily destroyed during cooking. To retain more vitamins, consider steaming, microwaving, or stir-frying foods instead of boiling them for extended periods.

3. Reduce cooking time: The longer you cook food, the more vitamins are lost. Cook vegetables just until they are tender-crisp to preserve their nutrient content. Avoid overcooking or boiling for a long time.

4. Use minimal water: When boiling or steaming vegetables, use the least amount of water necessary. This helps to minimize nutrient loss in the cooking water.

5. Store and prepare properly: Proper storage and preparation techniques can also help retain vitamins. Store fruits and vegetables in cool, dark places to slow down vitamin degradation. Cut fruits and vegetables just before consuming to minimize exposure to air and light, which can degrade vitamins.

6. Eat raw or lightly cooked foods: Some vitamins, like vitamin C, are heat-sensitive and can be partially destroyed during cooking. Consuming raw or lightly cooked fruits and vegetables can help retain their vitamin content.

7. Consider alternative cooking methods: Some cooking methods, such as grilling, broiling, or roasting, may lead to the loss of certain vitamins. Consider incorporating alternative cooking methods like steaming or sautéing to retain more nutrients.

It's important to note that some vitamins are water-soluble and can be leached out during cooking. Consuming the cooking water or using it in soups and sauces can help retain some of those lost vitamins.

Remember, the specific vitamin content in food can vary depending on various factors such as food quality, storage conditions, and cooking methods.