Choose a celery root that seems heavy for its size.
In a small bowl, combine mustard and vinegar. Slowly drizzle in olive oil, and whisk until mixture is creamy. Season to taste with salt and pepper.
Peel celery root with a sharp knife. Cut root in half crosswise and slice each half as thinly as possible. Keep slices in a bowl of cold water until needed. Drain and pat dry when ready to toss with the vinaigrette.
Place vegetables in separate bowls, season with salt and pepper, and toss well. Add about 1 1/2 teaspoons dressing to each bowl and toss again. Arrange vegetables in separate piles on salad plates and serve immediately.